On hom-algebras with surjective twisting
By Aron Gohr. 2009
111 citations recorded by the source corpus.
Abstract A hom-associative structure is a set A together with a binary operation ⋆ and a self-map α such that an α -twisted version of associativity is fulfilled. In this paper, we assume that α is surjective. We show that in this case, under surprisingly weak additional conditions on the multiplication, the binary operation is a twisted version of an associative operation. As an application, an earlier result (Fregier and Gohr [1] ) on weakly unital hom-algebras is recovered with a different proof. In the second section, consequences for the deformation theory of hom-algebras with surjective twisting map are discussed.
Subfields: Algebra and Number Theory, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/404f54719c24a022c804363e1c41a80a91cf3aad
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In Algebra and Number Theory
- Abdenacer Makhlouf
- Donald Yau
- Florin Panaite
- Aron Gohr
- Sergei Silvestrov
- Yael Fregier
- Stefaan Caenepeel
- I. Goyvaerts
In Geometry and Topology
- Abdenacer Makhlouf
- Donald Yau
- Florin Panaite
- Aron Gohr
- Sergei Silvestrov
- Stefaan Caenepeel
- I. Goyvaerts
- Yael Fregier
Citations in the corpus
- Monoidal Hom–Hopf Algebras (2009, background): “Gohr [4] calls A a twist if there is an associative multiplication · on A such that a ∗ b = a · b , for all a b ∈ A.”
- Universal Algebra of a Hom-Lie Algebra and group-like elements (2015, background): “ i.e. the quotient g/k inherits a structure of Hom-Lie algebra. By construction, its induced morphism α: g/k → g/k is invertible. The induced bracket α−1 ◦ [,] is therefore a Lie algebra bracket, see [G]. Also, the natural projection g/kis a morphism of Hom-Lie algebra. Definition 1.3. [MS1] A Hom-as”
- Hom-bialgebras and comodule Hom-algebras (2008, background): “3,14,15,22,23], 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 are rel”
- Unital algebras of Hom-associative type and surjective or injective twistings (2009, background): “It should be noted however that in Hom-associative structures, several types of unitality make sense as was observed in [3, 4, 5, 6].”
- Yetter-Drinfeld modules for Hom-bialgebras (2013, background): “See also [15, 16] for other properties of Hom-associative algebras.”
- 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.”
- Paradigm of Nonassociative Hom-algebras and Hom-superalgebras (2010, methodology): “This question was addressed and discussed for Hom-associative algebras in [18, 19].”
- Rota–Baxter Hom-Lie–Admissible Algebras (2011, background): “Following the observation in [38], when is invertible, the twisting principle with −1 leads to a G-associative algebra.”