We study Virasoro-type extensions of the q-deformed Witt Hom–Lie superalgebras. Moreover, we provide the cohomology of q-deformed Witt–Virasoro superalgebras of the Hom type.
Similar content being viewed by others
References
F. Ammar and A. Makhlouf, “Hom–Lie algebras and Hom–Lie admissible superalgebras,” J. Algebra, 324, No. 7, 1513–1528 (2010).
F. Ammar, A. Makhlouf, and N. Saadaoui, “Cohomology of Hom–Lie superalgebras and q-deformed Witt superalgebra,” Czechoslovak Math. J., 63, No. 138 (2013).
F. Ammar, A. Makhlouf, and N. Saadaoui, “Second cohomology of q-deformed Witt superalgebras,” J. Math. Phys., 54 (2013).
A. Fialowski and M. Penkava, “Extensions of (super) Lie algebra,” Comm. Contemp. Math., 11, No. 5, 709–737 (2009).
N. Hijligenberg and Y. Kotchetkov, “The absolute rigidity of the Neveu–Schwarz and Ramond superalgebras,” J. Math. Phys., 37, 5858 (1996).
Y. Cheng and H. Yang, “Low-dimensional cohomology of q-deformed Heisenberg–Virasoro algebra of Hom-type,” Front. Math. China, 5, Issue 4, 607–622 (2010).
D. Larsson and S. D. Silvestrov, “Quasi-Hom-Lie algebras, central extensions, and 2-cocycle-like identities,” J. Algebra, 288, 321–344 (2005).
A. Makhlouf and S. D. Silvestrov, “Hom-algebra structures,” J. Gen. Lie Theory Appl., 2, No. 2, 51–64 (2008).
A. Fialowski and M. Schlichenmaier, “Global deformations of theWitt algebra of Krichever–Novikov type,” Comm. Contemp. Math., 5, No. 6, 921–945 (2003).
A. Fialowski, “Formal rigidity of the Witt and Virasoro algebra,” J. Math. Phys., 53, No. 7 (2012).
M. Penkava, “L∞ algebras and their cohomology,” arXiv. 9512014 (1995).
M. Schlichenmaier, “An elementary proof of the vanishing of the second cohomology of the Witt and Virasoro algebra with values in the adjoint module,” Forum Math., 26, No. 3, 913–929 (2014).
M. Schlichenmaier, “Krichever–Novikov type algebras,” De Gruyter Stud. Math., 53 (2014).
Y. Sheng, “Representations of Hom–Lie algebras,” Algebr. Represent. Theory, 15, No. 6, 1081–1098 (2012).
M. Scheunert and R. B. Zhang, “Cohomology of Lie superalgebras and their generalizations,” J. Math. Phys., 39, No. 9, 5024–5061 (1998).
D. Yau, “Enveloping algebra of Hom–Lie algebras,” J. Gen. Lie Theory Appl., 2, No. 2, 95–108 (2008).
Author information
Authors and Affiliations
Corresponding author
Additional information
Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 71, No. 11, pp. 1539–1552, November, 2019.
Rights and permissions
About this article
Cite this article
Makhlouf, A., Saadaoui, N. Cohomology of q-Deformed Witt–Virasoro Superalgebras of the Hom Type. Ukr Math J 71, 1763–1780 (2020). https://doi.org/10.1007/s11253-020-01746-5
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11253-020-01746-5