Unital algebras of Hom-associative type and surjective or injective twistings
By Yael Fregier, Aron Gohr, Sergei Silvestrov. 2009
60 citations recorded by the source corpus.
In this paper, we introduce a common generalizing framework for alternative types of Hom-associative algebras. We show that the observation that unital Hom-associative algebras with surjective or injective twisting map are already associative has a generalization in this new framework. We also show by construction of a counterexample that another such generalization fails even in a very restricted particular case. Finally, we discuss an application of these observations by answering in the negative the question whether nonassociative algebras with unit such as the octonions may be twisted by the composition trick into Hom-associative algebras.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/471134a8d255107d7bf5aac5666c5727c51433ce
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In Algebra and Number Theory
- Florin Panaite
- Stefaan Caenepeel
- I. Goyvaerts
- Abdenacer Makhlouf
- Donald Yau
- Y. Sheng
- Sergei Silvestrov
- F. Ammar
In Geometry and Topology
- Florin Panaite
- Stefaan Caenepeel
- I. Goyvaerts
- Abdenacer Makhlouf
- Donald Yau
- Michael E. Hoffman
- Y. Sheng
- F. Ammar
In Mathematical Physics
- Florin Panaite
- Stefaan Caenepeel
- I. Goyvaerts
- Abdenacer Makhlouf
- Donald Yau
- Y. Sheng
- F. Ammar
- Marcelo Muniz Silva Alves
Citations in the corpus
- Yetter-Drinfeld modules for Hom-bialgebras (2013, background): “See also [15, 16] for other properties of Hom-associative algebras.”
- Monoidal Hom–Hopf Algebras (2009, background): “Sufficient conditions for A to be a twist are discussed in great detail in [1, 2, 3, 4].”