Abstract
We construct a generalization of the BGG-category O, whose blocks correspond to standardly stratified algebras. We prove reciprocity formulae in these categories and present two classes of examples.
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Ágoston, I., Dlab, V. and Lukács, E.: Stratified algebras, C.R. Math. Rep. Acad. Sci. Canada 20(1) (1998), 22-28.
Ágoston, I., Dlab, V. and Lukács, E.: Strictly stratified algebras, In: Algebra. Proc. Kurosh Internat. Algebraic Conf., W. de Gruyter, Berlin, 2000, pp. 17-26.
Bernstein, I. N., Gelfand, I. M. and Gelfand, S. I.: A certain category of G-modules (Russian), Funktsional. Anal. i Prilozhen. 10(2) (1976) 1-8.
Cline, E., Parshall, B. and Scott, L.: Finite-dimensional algebras and highest weight categories, J. Reine Angew. Math. 391 (1988), 85-99.
Cline, E., Parshall, B. and Scott, L.: Stratifying endomorphism algebras, Mem. Amer. Math. Soc. 124(591) (1996).
Coleman, A. J. and Futorny, V.: Stratified L-modules, J. Algebra 163 (1994), 219-234.
Dixmier, J.: Algèbres enveloppantes, Paris, 1974.
Dlab, V.: Quasi-hereditary algebras revisited. Representation theory of groups, algebras, and orders, An. XX¸Stiint. Univ. Ovidius ConstanXX¸ta Ser. Mat. 4 (1996), 43-54.
Dlab, V.: Properly stratified algebras, C.R. Acad. Sci. Paris, to appear.
Drozd, Yu. A., Futorny, V. M. and Ovsienko, S. A.: The Harish-Chandra S-homomorphism and G-modules generated by a semiprimitive element (Russian), Ukraïn. Mat. Zh. 42(8) (1990), 1031-1037; transl. in Ukrainian Math. J. 42(8) (1990), 919-924.
Drozd, Yu. A., Futorny, V. M. and Ovsienko, S. A.: Harish-Chandra subalgebras and Gelfand-Zetlin modules, In: Finite-Dimensional Algebras and Related Topics (Ottawa, ON, 1992), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci. 424, Kluwer Acad. Publ., Dordrecht, 1994, pp. 79-93.
Futorny, V. and Pollack, D.: A new category of Lie algebra modules satisfying the BGG reciprocity principle, Comm. Algebra 22(1) (1994), 213-227.
Futorny, V. and Mazorchuk, V.: Highest weight categories of Lie algebra modules, J. Pure Appl. Algebra 138(2) (1999), 107-118.
Gomez, X. and Mazorchuk, V.: On an analogue of BGG-reciprocity, Preprint CPT-99/P.3882, Marseille University.
Irving, R.: BGG algebras and the BGG reciprocity principle, J. Algebra 135(2) (1990), 363-380.
Klucznik, M. and Mazorchuk, V.: Parabolic decomposition for projectively stratified algebras, Preprint 99-083, SFB 343, Bielefeld.
Kostant, B.: On the tensor product of a finite and an infinite dimensional representation, J. Funct. Anal. 20(4) (1975), 257-285.
Mazorchuk, V. and Ovsienko, S.: Submodule structure of generalized Verma modules induced from generic Gelfand-Zetlin modules, Algebras Represent. Theory 1(1) (1998), 3-26.
Rocha-Caridi, A.: Splitting criteria for G-modules induced from a parabolic and the Bernstein-Gelfand-Gelfand resolution of a finite-dimensional, irreducible G-module, Trans. Amer. Math. Soc. 262(2) (1980), 335-366.
Rocha-Caridi, A. and Wallach, N.: Projective modules over graded Lie algebras, I, Math. Z. 180(2) (1982), 151-177.
Soergel, W.: The combinatorics of Harish-Chandra bimodules, J. Reine Angew. Math. 429 (1992), 49-74.
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Futorny, V., König, S. & Mazorchuk, V. Categories of Induced Modules and Standardly Stratified Algebras. Algebras and Representation Theory 5, 259–276 (2002). https://doi.org/10.1023/A:1016579318115
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DOI: https://doi.org/10.1023/A:1016579318115