On Hom-algebra structures
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Publication:6477879
DOI10.4303/JGLTA/S070206arXivmath/0609501WikidataQ115206433 ScholiaQ115206433MaRDI QIDQ6477879
Sergei Silvestrov, Abdenacer Makhlouf
Publication date: 18 September 2006
Abstract: A Hom-algebra structure is a multiplication on a vector space where the structure is twisted by a homomorphism. The structure of Hom-Lie algebra was introduced by Hartwig, Larsson and Silvestrov and extended by Larsson and Silvestrov to quasi-hom Lie and quasi-Lie algebras. In this paper we introduce and study Hom-associative, Hom-Leibniz, and Hom-Lie admissible algebraic structures which generalize the well known associative, Leibniz and Lie admissible algebras. Also, we characterize the flexible Hom-algebras in this case. We also explain some connections between Hom-Lie algebras and Santilli's isotopies of associative and Lie algebras.
Leibniz algebras (17A32) Nonassociative algebras satisfying other identities (17A30) Generalizations (16Y99)
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