Hom-Lie Superalgebras and Hom-Lie admissible Superalgebras
By F. Ammar, Abdenacer Makhlouf. 2009
178 citations recorded by the source corpus.
The purpose of this paper is to study Hom-Lie superalgebras, that is a superspace with a bracket for which the superJacobi identity is twisted by a homomorphism. This class is a particular case of $\Gamma$-graded quasi-Lie algebras introduced by Larsson and Silvestrov. In this paper, we characterize Hom-Lie admissible superalgebras and provide a construction theorem from which we derive a one parameter family of Hom-Lie superalgebras deforming the orthosymplectic Lie superalgebra. Also, we prove a $\mathbb{Z}_2$-graded version of a Hartwig-Larsson-Silvestrov Theorem which leads us to a construction of a q-deformed Witt superalgebra.
Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/fe9aaade04cb0f56e346b78e5135d9bcef6fb450
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In Algebra and Number Theory
- Abdenacer Makhlouf
- Donald Yau
- Aron Gohr
- Sergei Silvestrov
- Yael Fregier
- Florin Panaite
- F. Ammar
- Y. Sheng
In Geometry and Topology
- Abdenacer Makhlouf
- Donald Yau
- Aron Gohr
- Sergei Silvestrov
- Yael Fregier
- Florin Panaite
- F. Ammar
- Y. Sheng
In Statistical and Nonlinear Physics
Citations in the corpus
- Hom-bialgebras and comodule Hom-algebras (2008, background): “ [8,13,14,15,22,23], number theory [12], the various versionsof the Yang-Baxter equations, braid group representations, and quantum groups [28] - [35]. Other papers concerning Hom-type structures are [2]- [7], [10], [17] - [21], and [24] - [27]. A fundamental property of Lie algebras is that they ar”
- Paradigm of Nonassociative Hom-algebras and Hom-superalgebras (2010, methodology): “13 (A q-deformed Witt superalgebra, [4]).”
- Unital algebras of Hom-associative type and surjective or injective twistings (2009, background): “At the same time, on the side of algebra structures, formal deformations and elements of co-homology for Hom-associative and Hom-Lie algebras have been considered by Makhlouf and Silvestrov in [18], and elements of homology for Hom-algebras have been considered by Yau in [20].”
- HOM-ALTERNATIVE ALGEBRAS AND HOM-JORDAN ALGEBRAS (2009, background): “See also [2,3,8,9,10,19,29] for other works on twisted algebraic structures.”