Cohomology of Hom-Lie superalgebras and q -deformed Witt superalgebra

Faouzi Ammar; Abdenacer Makhlouf; Nejib Saadaoui

Czechoslovak Mathematical Journal (2013)

  • Volume: 63, Issue: 3, page 721-761
  • ISSN: 0011-4642

Abstract

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Hom-Lie algebra (superalgebra) structure appeared naturally in q -deformations, based on σ -derivations of Witt and Virasoro algebras (superalgebras). They are a twisted version of Lie algebras (superalgebras), obtained by deforming the Jacobi identity by a homomorphism. In this paper, we discuss the concept of α k -derivation, a representation theory, and provide a cohomology complex of Hom-Lie superalgebras. Moreover, we study central extensions. As application, we compute derivations and the second cohomology group of a twisted osp ( 1 , 2 ) superalgebra and q -deformed Witt superalgebra.

How to cite

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Ammar, Faouzi, Makhlouf, Abdenacer, and Saadaoui, Nejib. "Cohomology of Hom-Lie superalgebras and $q$-deformed Witt superalgebra." Czechoslovak Mathematical Journal 63.3 (2013): 721-761. <http://eudml.org/doc/260611>.

@article{Ammar2013,
abstract = {Hom-Lie algebra (superalgebra) structure appeared naturally in $q$-deformations, based on $\sigma $-derivations of Witt and Virasoro algebras (superalgebras). They are a twisted version of Lie algebras (superalgebras), obtained by deforming the Jacobi identity by a homomorphism. In this paper, we discuss the concept of $\alpha ^k$-derivation, a representation theory, and provide a cohomology complex of Hom-Lie superalgebras. Moreover, we study central extensions. As application, we compute derivations and the second cohomology group of a twisted $\{\rm osp\}(1,2)$ superalgebra and $q$-deformed Witt superalgebra.},
author = {Ammar, Faouzi, Makhlouf, Abdenacer, Saadaoui, Nejib},
journal = {Czechoslovak Mathematical Journal},
keywords = {Hom-Lie superalgebra; derivation; cohomology; $q$-deformed superalgebra; Hom-Lie superalgebra; cohomology; -deformed superalgebra},
language = {eng},
number = {3},
pages = {721-761},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Cohomology of Hom-Lie superalgebras and $q$-deformed Witt superalgebra},
url = {http://eudml.org/doc/260611},
volume = {63},
year = {2013},
}

TY - JOUR
AU - Ammar, Faouzi
AU - Makhlouf, Abdenacer
AU - Saadaoui, Nejib
TI - Cohomology of Hom-Lie superalgebras and $q$-deformed Witt superalgebra
JO - Czechoslovak Mathematical Journal
PY - 2013
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 63
IS - 3
SP - 721
EP - 761
AB - Hom-Lie algebra (superalgebra) structure appeared naturally in $q$-deformations, based on $\sigma $-derivations of Witt and Virasoro algebras (superalgebras). They are a twisted version of Lie algebras (superalgebras), obtained by deforming the Jacobi identity by a homomorphism. In this paper, we discuss the concept of $\alpha ^k$-derivation, a representation theory, and provide a cohomology complex of Hom-Lie superalgebras. Moreover, we study central extensions. As application, we compute derivations and the second cohomology group of a twisted ${\rm osp}(1,2)$ superalgebra and $q$-deformed Witt superalgebra.
LA - eng
KW - Hom-Lie superalgebra; derivation; cohomology; $q$-deformed superalgebra; Hom-Lie superalgebra; cohomology; -deformed superalgebra
UR - http://eudml.org/doc/260611
ER -

References

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