Quasi-Lie algebras

By Daniel S. D. Larsson, Sergei Silvestrov. 2004

135 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/73edca2394fa9f054e14f6801d29dca214bf92e1

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In Algebra and Number Theory

In Discrete Mathematics and Combinatorics

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Citations in the corpus

Yetter-Drinfeld modules for Hom-bialgebras (2013, methodology): “Motivated by these examples and their generalization, Hartwig, Larsson and Silvestrov in [17, 21, 22, 23] introduced the notion of Hom-Lie algebra as a deformation of Lie algebras in which the Jacobi identity is twisted by a homomorphism.”
Hom-Lie Superalgebras and Hom-Lie admissible Superalgebras (2009, methodology): “Also, we recall the definition of quasi-Lie algebras (see [13]) which border Hom-Lie algebras, Hom-Lie superalgebras and color Lie algebras, as well as quasi-hom-Lie algebras appearing naturally in the study of σ-derivations.”
Hom-bialgebras and comodule Hom-algebras (2008, background): “Hom-Lie algebras are also related to deformed vector fields [8,13,14,15,22,23], number theory [12], the various versions of the Yang-Baxter equations, braid group representations, and quantum groups [28] - [35].”
Representations of Hom-Lie Algebras (2010, background): “Because of close relation to discrete and deformed vector fields and differential calculus [5, 7, 8], hom-Lie algebras are widely studied recently [1, 2, 9, 10, 12, 13, 14].”
BiHom-associative algebras, BiHom-Lie algebras and BiHom-bialgebras (2015, background): “Hartwig, Larsson and Silvestrov studied this kind of algebras in [17, 22, 23, 24] and called them Hom-Lie algebras because they involve a homomorphism in the defining identity.”
HOM-ALTERNATIVE ALGEBRAS AND HOM-JORDAN ALGEBRAS (2009, methodology): “The Hom-Lie algebras were introduced and discussed in [12,14,15,16], motivated by quasi-deformations of Lie algebras of vector fields, in particular q-deformations of Witt and Virasoro algebras.”
On Hom-algebra structures (2006, methodology): “It had been shown in [4, 5, 6, 7] that the class of quasi-Hom-Lie algebras contains as a subclass on one hand the color Lie algebras and in particular Lie superalgebras and Lie algebras, and on another hand various known and new single and multi-parameter families of algebras obtained using twisted ”
Unital algebras of Hom-associative type and surjective or injective twistings (2009, background): “In [7, 8, 12], quasi-Hom-Lie algebras, the general quasi-Lie algebras, and the corresponding generalization of Leibniz algebras quasi-Leibniz algebras [9] have been introduced.”
Quasi-Deformations of 𝔰𝔩2(𝔽) Using Twisted Derivations (2005, methodology): “With this definition quasiLie algebras include not only hom-Lie algebras as a subclass, but also color Lie algebras and in particular Lie super-algebras (Larsson and Silvestrov, 2005a).”
Hom-algebras and homology (2007, background): “Hom-Lie algebras are closely related to discrete and deformed vector fields and differential calculus [14, 18, 19].”