On Hom-algebra structures
On Hom-algebra structures
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DOI：
10.4303/jglta/s070206
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发表时间：
2006-09
期刊：
影响因子：
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通讯作者：
Abdenacer Makhlouf;S. Silvestrov
中科院分区：
文献类型：
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作者：
Abdenacer Makhlouf;S. Silvestrov
Hom-algebra结构是向量空间上的乘法，其中该结构被同态扭曲。Hom-李代数的结构由Hartwig，Larsson和Silvestrov引入，并由Larsson和Silvestrov推广到拟Hom李和拟李代数。本文引入并研究了Hom-associative、Hom-Leibniz和Hom-Lie容许代数结构，它们推广了著名的结合、Leibniz和Lie容许代数。同时，我们刻画了这种情形下的柔性Hom-代数。我们还解释了Hom-Lie代数和结合李代数的Rollli同位素之间的一些联系。
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.