On Hom type algebras

Abstract

Hom-algebras are generalizations of algebras obtained using a twisting by a linear map. But there is a priori a freedom on where to twist. We enumerate here all the possible choices in the Lie and associative categories and study the relations between the obtained algebras. The associative case is richer since it admits the notion of unit element. We use this fact to find sufficient conditions for hom-associative algebras to be associative and classify the implications between the hom-associative types of unital algebras.

24 pages. Final version submitted for publication

References in corpus (7)

• Deformations of Lie Algebras using $\sigma$-derivations
• Hom-algebras and homology
• Notes on Formal Deformations of Hom-associative and Hom-Lie Algebras
• On unitality conditions for Hom-associative algebras
• Quasi-Deformations of sl_2(\F) using twisted derivations
• Hom-Algebras and Hom-Coalgebras
• On hom-algebras with surjective twisting

Cited by in corpus (15)

• Hom-bialgebras and comodule Hom-algebras
• Hom-quantum groups I: quasi-triangular Hom-bialgebras
• The classical Hom-Yang-Baxter equation and Hom-Lie bialgebras
• Hom-quantum groups II: cobraided Hom-bialgebras and Hom-quantum geometry
• Hom-quantum groups III: Representations and module Hom-algebras
• Paradigm of Nonassociative Hom-algebras and Hom-superalgebras
• Hom-alternative algebras and Hom-Jordan algebras
• Deformations of Hom-Alternative and Hom-Malcev algebras
• Hom-Lie Superalgebras and Hom-Lie admissible Superalgebras
• Infinitesimal Hom-bialgebras and Hom-Lie bialgebras
• Hom-algebras via PROPs
• On Koszulity for operads of Conformal Field Theory
• Hom-Akivis algebras
• Quadratic and symplectic structures on 3-(Hom)-$\rho$-Lie algebras
• (Bi)Hom-Leibniz algebras