E. Cremmer, B. Julia, H. Lü and C.N. Pope, Dualization of dualities. 1, Nucl. Phys.
B 523 (1998) 73 [hep-th/9710119] [INSPIRE].
ADS
MATH
Article
Google Scholar
E. Cremmer, B. Julia, H. Lü and C.N. Pope, Dualization of dualities. 2. Twisted self-duality of doubled fields and superdualities, Nucl. Phys.
B 535 (1998) 242 [hep-th/9806106] [INSPIRE].
ADS
MATH
Article
Google Scholar
P. Henry-Labordere, B. Julia and L. Paulot, Borcherds symmetries in M-theory, JHEP
04 (2002) 049 [hep-th/0203070] [INSPIRE].
ADS
MathSciNet
Article
Google Scholar
P. Henry-Labordere, B. Julia and L. Paulot, Real Borcherds superalgebras and M-theory, JHEP
04 (2003) 060 [hep-th/0212346] [INSPIRE].
ADS
MathSciNet
Article
Google Scholar
B.L. Julia, Dualities in the classical supergravity limits: dualizations, dualities and a detour via (4k + 2)-dimensions, hep-th/9805083 [INSPIRE].
P.C. West, E
11
and M-theory, Class. Quant. Grav.
18 (2001) 4443 [hep-th/0104081] [INSPIRE].
ADS
MATH
Article
Google Scholar
T. Damour, M. Henneaux and H. Nicolai, E
10
and a ‘small tension expansion’ of M-theory, Phys. Rev. Lett.
89 (2002) 221601 [hep-th/0207267] [INSPIRE].
ADS
MathSciNet
MATH
Article
Google Scholar
F. Riccioni and P.C. West, The E
11
origin of all maximal supergravities, JHEP
07 (2007) 063 [arXiv:0705.0752] [INSPIRE].
ADS
Article
Google Scholar
E.A. Bergshoeff, I. De Baetselier and T.A. Nutma, E
11
and the embedding tensor, JHEP
09 (2007) 047 [arXiv:0705.1304] [INSPIRE].
ADS
Article
Google Scholar
E.A. Bergshoeff, J. Gomis, T.A. Nutma and D. Roest, Kac-Moody spectrum of (half-)maximal supergravities, JHEP
02 (2008) 069 [arXiv:0711.2035] [INSPIRE].
ADS
MathSciNet
Article
Google Scholar
F. Riccioni and P.C. West, E
11
-extended spacetime and gauged supergravities, JHEP
02 (2008) 039 [arXiv:0712.1795] [INSPIRE].
ADS
Article
Google Scholar
E.A. Bergshoeff, et al., E
10
and gauged maximal supergravity, JHEP
01 (2009) 020 [arXiv:0810.5767] [INSPIRE].
ADS
MATH
Article
Google Scholar
F. Riccioni, D. Steele and P. West, The E
11
origin of all maximal supergravities: the hierarchy of field-strengths, JHEP
09 (2009) 095 [arXiv:0906.1177] [INSPIRE].
ADS
Article
Google Scholar
E.A. Bergshoeff, M. de Roo, S.F. Kerstan and F. Riccioni, IIB supergravity revisited, JHEP
08 (2005) 098 [hep-th/0506013] [INSPIRE].
ADS
MathSciNet
Article
Google Scholar
E.A. Bergshoeff, M. de Roo, S.F. Kerstan, T. Ortín and F. Riccioni, IIA ten-forms and the gauge algebras of maximal supergravity theories, JHEP
07 (2006) 018 [hep-th/0602280] [INSPIRE].
ADS
MathSciNet
Article
Google Scholar
B. de Wit and H. Nicolai, N = 8 supergravity with local SO(8) × SU(8) invariance, Phys. Lett.
B 108 (1982) 285 [INSPIRE].
ADS
Article
Google Scholar
M. Günaydin, L.J. Romans and N.P. Warner, Gauged N = 8 supergravity in five-dimensions, Phys. Lett.
B 154 (1985) 268 [INSPIRE].
ADS
MathSciNet
Article
Google Scholar
M. Pernici, K. Pilch and P. van Nieuwenhuizen, Gauged maximally extended supergravity in seven-dimensions, Phys. Lett.
B 143 (1984) 103 [INSPIRE].
ADS
MathSciNet
Article
Google Scholar
C.M. Hull, Noncompact gaugings of N = 8 supergravity, Phys. Lett.
B 142 (1984) 39 [INSPIRE].
ADS
MathSciNet
Google Scholar
C.M. Hull, More gaugings of N = 8 supergravity, Phys. Lett.
B 148 (1984) 297 [INSPIRE].
ADS
MathSciNet
Article
Google Scholar
B. de Wit and H. Nicolai, The parallelizing S
7
torsion in gauged N = 8 supergravity, Nucl. Phys.
B 231 (1984) 506 [INSPIRE].
ADS
Article
Google Scholar
H. Nicolai and H. Samtleben, Maximal gauged supergravity in three-dimensions, Phys. Rev. Lett.
86 (2001) 1686 [hep-th/0010076] [INSPIRE].
ADS
MathSciNet
Article
Google Scholar
H. Nicolai and H. Samtleben, Compact and noncompact gauged maximal supergravities in three-dimensions, JHEP
04 (2001) 022 [hep-th/0103032] [INSPIRE].
ADS
MathSciNet
Article
Google Scholar
B. de Wit, H. Samtleben and M. Trigiante, On lagrangians and gaugings of maximal supergravities, Nucl. Phys.
B 655 (2003) 93 [hep-th/0212239] [INSPIRE].
ADS
MathSciNet
MATH
Article
Google Scholar
B. de Wit, H. Samtleben and M. Trigiante, Gauging maximal supergravities, Fortsch. Phys.
52 (2004) 489 [hep-th/0311225] [INSPIRE].
ADS
MathSciNet
MATH
Article
Google Scholar
B. de Wit and H. Samtleben, Gauged maximal supergravities and hierarchies of nonAbelian vector-tensor systems, Fortsch. Phys.
53 (2005) 442 [hep-th/0501243] [INSPIRE].
ADS
MathSciNet
MATH
Article
Google Scholar
B. de Wit, H. Nicolai and H. Samtleben, Gauged supergravities, tensor hierarchies and M-theory, JHEP
02 (2008) 044 [arXiv:0801.1294] [INSPIRE].
MathSciNet
Article
Google Scholar
B. de Wit and H. Samtleben, The end of the p-form hierarchy, JHEP
08 (2008) 015 [arXiv:0805.4767] [INSPIRE].
MathSciNet
Article
Google Scholar
H. Nicolai and H. Samtleben, N = 8 matter coupled AdS
3
supergravities, Phys. Lett.
B 514 (2001) 165 [hep-th/0106153] [INSPIRE].
ADS
MATH
Article
Google Scholar
B. de Wit, I. Herger and H. Samtleben, Gauged locally supersymmetric D = 3 nonlinear σ-models, Nucl. Phys.
B 671 (2003) 175 [hep-th/0307006] [INSPIRE].
ADS
MathSciNet
MATH
Article
Google Scholar
M. Weidner, Gauged supergravities in various spacetime dimensions, Fortsch. Phys.
55 (2007) 843 [hep-th/0702084] [INSPIRE].
ADS
MathSciNet
MATH
Article
Google Scholar
J. Greitz and P.S. Howe, Maximal supergravity in D = 10: forms, Borcherds algebras and superspace cohomology, JHEP
08 (2011) 146 [arXiv:1103.5053] [INSPIRE].
ADS
MathSciNet
MATH
Article
Google Scholar
J. Greitz and P.S. Howe, Half-maximal supergravity in three dimensions: supergeometry, differential forms and algebraic structure, JHEP
06 (2012) 177 [arXiv:1203.5585] [INSPIRE].
ADS
MathSciNet
MATH
Article
Google Scholar
J. Greitz and P.S. Howe, Maximal supergravity in three dimensions: supergeometry and differential forms, JHEP
07 (2011) 071 [arXiv:1103.2730] [INSPIRE].
ADS
MathSciNet
MATH
Article
Google Scholar
M. Henneaux, B.L. Julia and J. Levie, E
11
, Borcherds algebras and maximal supergravity, JHEP
04 (2012) 078 [arXiv:1007.5241] [INSPIRE].
ADS
MATH
Article
Google Scholar
J. Palmkvist, Tensor hierarchies, Borcherds algebras and E
11, JHEP
02 (2012) 066 [arXiv:1110.4892] [INSPIRE].
ADS
MathSciNet
MATH
Article
Google Scholar
A. Kleinschmidt and J. Palmkvist, Oxidizing Borcherds symmetries, JHEP
03 (2013) 044 [arXiv:1301.1346] [INSPIRE].
ADS
MathSciNet
MATH
Article
Google Scholar
J. Palmkvist, Borcherds and Kac-Moody extensions of simple finite-dimensional Lie algebras, JHEP
06 (2012) 003 [arXiv:1203.5107] [INSPIRE].
ADS
MathSciNet
Article
Google Scholar
M. Henneaux and V. Lekeu, Kac-Moody and Borcherds symmetries of six-dimensional chiral supergravity, JHEP
03 (2015) 056 [arXiv:1502.00518] [INSPIRE].
ADS
MathSciNet
Article
Google Scholar
J. Palmkvist, The tensor hierarchy algebra, J. Math. Phys.
55 (2014) 011701 [arXiv:1305.0018] [INSPIRE].
ADS
MathSciNet
MATH
Article
Google Scholar
J. Greitz, P. Howe and J. Palmkvist, The tensor hierarchy simplified, Class. Quant. Grav.
31 (2014) 087001 [arXiv:1308.4972] [INSPIRE].
ADS
MathSciNet
MATH
Article
Google Scholar
P.S. Howe, Supergravity in superspace, Nucl. Phys.
B 199 (1982) 309 [INSPIRE].
ADS
MathSciNet
Article
Google Scholar
E. Cremmer and S. Ferrara, Formulation of eleven-dimensional supergravity in superspace, Phys. Lett.
B 91 (1980) 61 [INSPIRE].
ADS
Article
Google Scholar
L. Brink and P.S. Howe, Eleven-dimensional supergravity on the mass-shell in superspace, Phys. Lett.
B 91 (1980) 384 [INSPIRE].
ADS
Article
Google Scholar
N. Dragon, Torsion and curvature in extended supergravity, Z. Phys.
C 2 (1979) 29 [INSPIRE].
ADS
MathSciNet
Google Scholar
P.S. Howe, Weyl superspace, Phys. Lett.
B 415 (1997) 149 [hep-th/9707184] [INSPIRE].
ADS
MathSciNet
Article
Google Scholar
A. Candiello and K. Lechner, Duality in supergravity theories, Nucl. Phys.
B 412 (1994) 479 [hep-th/9309143] [INSPIRE].
ADS
MathSciNet
MATH
Article
Google Scholar
M.F. Sohnius, Identities for Bianchi Identities, ICTP/79-80/44 (1979).
L. Bonora, P. Pasti and M. Tonin, Superspace formulation of 10-D SUGRA+SYM theory à la Green-Schwarz, Phys. Lett.
B 188 (1987) 335 [INSPIRE].
ADS
Google Scholar
M. Cederwall, B.E.W. Nilsson and D. Tsimpis, Spinorial cohomology and maximally supersymmetric theories, JHEP
02 (2002) 009 [hep-th/0110069] [INSPIRE].
ADS
MathSciNet
Article
Google Scholar
P.S. Howe and D. Tsimpis, On higher order corrections in M-theory, JHEP
09 (2003) 038 [hep-th/0305129] [INSPIRE].
ADS
MathSciNet
Article
Google Scholar
P.S. Howe, Pure spinors lines in superspace and ten-dimensional supersymmetric theories, Phys. Lett.
B 258 (1991) 141 [Addendum ibid.
B 259 (1991) 511] [INSPIRE].
P.S. Howe, Pure spinors, function superspaces and supergravity theories in ten-dimensions and eleven-dimensions, Phys. Lett.
B 273 (1991) 90 [INSPIRE].
ADS
MathSciNet
Article
Google Scholar
N. Berkovits, ICTP lectures on covariant quantization of the superstring, hep-th/0209059 [INSPIRE].
N. Berkovits and P.S. Howe, The cohomology of superspace, pure spinors and invariant integrals, JHEP
06 (2008) 046 [arXiv:0803.3024] [INSPIRE].
ADS
MathSciNet
Article
Google Scholar
F. Brandt, Supersymmetry algebra cohomology I: definition and general structure, J. Math. Phys.
51 (2010) 122302 [arXiv:0911.2118] [INSPIRE].
ADS
MathSciNet
MATH
Article
Google Scholar
F. Brandt, Supersymmetry algebra cohomology: II. Primitive elements in 2 and 3 dimensions, J. Math. Phys.
51 (2010) 112303 [arXiv:1004.2978] [INSPIRE].
ADS
MathSciNet
MATH
Article
Google Scholar
F. Brandt, Supersymmetry algebra cohomology III: Primitive elements in four and five dimensions, J. Math. Phys.
52 (2011) 052301 [arXiv:1005.2102] [INSPIRE].
ADS
MathSciNet
MATH
Article
Google Scholar
F. Brandt, Supersymmetry algebra cohomology IV: Primitive elements in all dimensions from D = 4 to D = 11, J. Math. Phys.
54 (2013) 052302 [arXiv:1303.6211] [INSPIRE].
ADS
MathSciNet
MATH
Article
Google Scholar
M.V. Movshev, A. Schwarz and R. Xu, Homology of Lie algebra of supersymmetries, arXiv:1011.4731 [INSPIRE].
M.V. Movshev, A. Schwarz and R. Xu, Homology of Lie algebra of supersymmetries and of super Poincaré Lie algebra, Nucl. Phys.
B 854 (2012) 483 [arXiv:1106.0335] [INSPIRE].
ADS
MATH
Article
Google Scholar
A. Achucarro, J.M. Evans, P.K. Townsend and D.L. Wiltshire, Super p-branes, Phys. Lett.
B 198 (1987) 441 [INSPIRE].
ADS
MathSciNet
Article
Google Scholar
E.A. Bergshoeff, J. Hartong, P.S. Howe, T. Ortín and F. Riccioni, IIA/IIB supergravity and ten-forms, JHEP
05 (2010) 061 [arXiv:1004.1348] [INSPIRE].
ADS
MathSciNet
MATH
Article
Google Scholar
P.S. Howe and P.C. West, The complete N = 2, D = 10 supergravity, Nucl. Phys.
B 238 (1984) 181 [INSPIRE].
ADS
MathSciNet
Article
Google Scholar
M. Cederwall, A. von Gussich, B.E.W. Nilsson, P. Sundell and A. Westerberg, The Dirichlet super p-branes in ten-dimensional type IIA and IIB supergravity, Nucl. Phys.
B 490 (1997) 179 [hep-th/9611159] [INSPIRE].
ADS
MathSciNet
MATH
Article
Google Scholar
G. Dall’Agata, K. Lechner and M. Tonin, D = 10, N = IIB supergravity: Lorentz invariant actions and duality, JHEP
07 (1998) 017 [hep-th/9806140] [INSPIRE].
ADS
MathSciNet
MATH
Article
Google Scholar
E. Bergshoeff, P.S. Howe, S. Kerstan and L. Wulff, Kappa-symmetric SL(2, ℝ) covariant D-brane actions, JHEP
10 (2007) 050 [arXiv:0708.2722] [INSPIRE].
ADS
MathSciNet
Article
Google Scholar
R. Slansky, An algebraic role for energy and number operators for multiparticle states, Nucl. Phys.
B 389 (1993) 349 [INSPIRE].
ADS
MathSciNet
Article
Google Scholar
I. Bandos and T. Ortin, Tensor gauge fields of N = 8 supergravity, Phys. Rev.
D 91 (2015) 085031 [arXiv:1502.00649] [INSPIRE].
ADS
MathSciNet
Google Scholar
B.E.W. Nilsson and A.K. Tollsten, The geometrical off-shell structure of pure N = 1 D = 10 supergravity in superspace, Phys. Lett.
B 169 (1986) 369 [INSPIRE].
ADS
MathSciNet
Article
Google Scholar
P.S. Howe and A. Umerski, On superspace supergravity in ten-dimensions, Phys. Lett.
B 177 (1986) 163 [INSPIRE].
ADS
MathSciNet
Article
Google Scholar
E. Bergshoeff, M. de Roo and B. de Wit, Extended conformal supergravity, Nucl. Phys.
B 182 (1981) 173 [INSPIRE].
ADS
MathSciNet
Article
Google Scholar
P.S. Howe and U. Lindström, The supercurrent in five-dimensions, Phys. Lett.
B 103 (1981) 422 [INSPIRE].
ADS
Article
Google Scholar
E. Bergshoeff, M. de Roo, B. de Wit and P. van Nieuwenhuizen, Ten-dimensional maxwell-einstein supergravity, its currents and the issue of its auxiliary fields, Nucl. Phys.
B 195 (1982) 97 [INSPIRE].
ADS
MATH
Article
Google Scholar
E. Bergshoeff and M. de Roo, The supercurrent in ten-dimensions, Phys. Lett.
B 112 (1982) 53 [INSPIRE].
ADS
Article
Google Scholar
P.S. Howe, H. Nicolai and A. Van Proeyen, Auxiliary fields and a superspace lagrangian for linearized ten-dimensional supergravity, Phys. Lett.
B 112 (1982) 446 [INSPIRE].
ADS
Article
Google Scholar
P.S. Howe, A superspace approach to extended conformal supergravity, Phys. Lett.
B 100 (1981) 389 [INSPIRE].
ADS
MathSciNet
Article
Google Scholar
P.S. Howe, J.M. Izquierdo, G. Papadopoulos and P.K. Townsend, New supergravities with central charges and Killing spinors in (2 + 1)-dimensions, Nucl. Phys.
B 467 (1996) 183 [hep-th/9505032] [INSPIRE].
ADS
MathSciNet
MATH
Article
Google Scholar
S.M. Kuzenko, U. Lindström and G. Tartaglino-Mazzucchelli, Off-shell supergravity-matter couplings in three dimensions, JHEP
03 (2011) 120 [arXiv:1101.4013] [INSPIRE].
ADS
MathSciNet
MATH
Article
Google Scholar
M. Cederwall, U. Gran and B.E.W. Nilsson, D = 3, N = 8 conformal supergravity and the Dragon window, JHEP
09 (2011) 101 [arXiv:1103.4530] [INSPIRE].
ADS
MathSciNet
MATH
Article
Google Scholar
B.E.W. Nilsson, Simple ten-dimensional supergravity in superspace, Nucl. Phys.
B 188 (1981) 176 [INSPIRE].
ADS
Article
Google Scholar
S. Bellucci and S.J. Gates Jr., D = 10, N = 1 superspace supergravity and the Lorentz Chern-Simons form, Phys. Lett.
B 208 (1988) 456 [INSPIRE].
ADS
MathSciNet
Article
Google Scholar
K. Lechner and M. Tonin, Superspace formulations of ten-dimensional supergravity, JHEP
06 (2008) 021 [arXiv:0802.3869] [INSPIRE].
ADS
MathSciNet
Article
Google Scholar
P.S. Howe, Heterotic supergeometry revisited, arXiv:0805.2893 [INSPIRE].
S.J. Gates Jr., Ectoplasm has no topology: the prelude, in Dubna 1997, Supersymmetries and quantum symmetries, E. Ivanov et al. eds., Lecture Notes in Physics, Spinger (1997), hep-th/9709104 [INSPIRE].
S.J. Gates Jr., M.T. Grisaru, M.E. Knutt-Wehlau and W. Siegel, Component actions from curved superspace: normal coordinates and ectoplasm, Phys. Lett.
B 421 (1998) 203 [hep-th/9711151] [INSPIRE].
ADS
MathSciNet
Article
Google Scholar
P.S. Howe, G. Sierra and P.K. Townsend, Supersymmetry in six-dimensions, Nucl. Phys.
B 221 (1983) 331 [INSPIRE].
ADS
MathSciNet
Article
Google Scholar
M. Cederwall and J. Palmkvist, Borcherds superalgebras, constraints and partition functions, to appear.
A. Le Diffon and H. Samtleben, Supergravities without an action: gauging the trombone, Nucl. Phys.
B 811 (2009) 1 [arXiv:0809.5180] [INSPIRE].
ADS
MathSciNet
MATH
Article
Google Scholar
F. Riccioni, Local E
11
and the gauging of the trombone symmetry, Class. Quant. Grav.
27 (2010) 125009 [arXiv:1001.1316] [INSPIRE].
ADS
MATH
Article
Google Scholar
J.J. Fernandez-Melgarejo, T. Ortín and E. Torrente-Lujan, Maximal nine dimensional supergravity, general gaugings and the embedding tensor, Fortsch. Phys.
60 (2012) 1012 [arXiv:1209.3774] [INSPIRE].
ADS
MathSciNet
MATH
Article
Google Scholar
H. J. Prins, Gauging the half-maximal trombone in 4D (2014).
L.J. Romans, Massive N = 2a supergravity in ten-dimensions, Phys. Lett.
B 169 (1986) 374 [INSPIRE].
ADS
Article
Google Scholar
P.S. Howe, N.D. Lambert and P.C. West, A new massive type IIA supergravity from compactification, Phys. Lett.
B 416 (1998) 303 [hep-th/9707139] [INSPIRE].
ADS
MathSciNet
Article
Google Scholar
I.V. Lavrinenko, H. Lü and C.N. Pope, Fiber bundles and generalized dimensional reduction, Class. Quant. Grav.
15 (1998) 2239 [hep-th/9710243] [INSPIRE].
ADS
MATH
Article
Google Scholar
I.V. Lavrinenko, H. Lü, C.N. Pope and K.S. Stelle, Superdualities, brane tensions and massive IIA/IIB duality, Nucl. Phys.
B 555 (1999) 201 [hep-th/9903057] [INSPIRE].
ADS
MathSciNet
MATH
Article
Google Scholar
M.J. Duff, J.T. Liu and R. Minasian, Eleven-dimensional origin of string-string duality: a one loop test, Nucl. Phys.
B 452 (1995) 261 [hep-th/9506126] [INSPIRE].
ADS
MathSciNet
MATH
Article
Google Scholar
P.S. Howe and U. Lindström, Higher order invariants in extended supergravity, Nucl. Phys.
B 181 (1981) 487 [INSPIRE].
ADS
Article
Google Scholar
W. Siegel, On-shell O(N) supergravity in superspace, Nucl. Phys.
B 177 (1981) 325 [INSPIRE].
ADS
MathSciNet
Article
Google Scholar
V.G. Kac, A sketch of Lie superalgebra theory, Commun. Math. Phys.
53 (1977) 31 [INSPIRE].
ADS
MathSciNet
MATH
Article
Google Scholar
V.G. Kac, Lie superalgebras, Adv. Math.
26 (1977) 8 [INSPIRE].
MATH
Article
Google Scholar
U. Ray, A character formula for generalized Kac-Moody superalgebras, J. Algebra.
177 (1995) 154.
MathSciNet
MATH
Article
Google Scholar
U. Ray, Automorphic forms and Lie superalgebras, Springer, Germany (2006).
MATH
Google Scholar
M. Wakimoto, Infinite-dimensional Lie algebras, American Mathematical Society, U.S.A. (2001).
MATH
Book
Google Scholar
V.G. Kac, Simple irreducible graded Lie algebras of finite growth, Izv. AN USSR
32 (1968) 1923.
MathSciNet
Google Scholar
R.E. Borcherds, Generalized Kac-Moody algebras, J. Algebra
115 (1988) 501.
MathSciNet
MATH
Article
Google Scholar
V.G. Kac, Infinite dimensional Lie algebras, 3rd edition, Cambridge University Press, Cambridge U.K. (1990).
MATH
Book
Google Scholar
L. Frappat, A. Sciarrino and P. Sorba, Dictionary on Lie algebras and superalgebras. Academic Press, U.S.A. (2000).
MATH
Google Scholar
D.A. Leites, M.V. Saveliev and V.V. Serganova, Embeddings of Lie superalgebra osp(1|2) and the associated nonlinear supersymmetric equations, in Group theoretical methods in physics, M.A. Markov et al. eds., VUN Science Press (1986).