| On the Structures of Hom-Lie Algebras |
| Received:December 01, 2012 Revised:April 16, 2014 |
| Key Words:
Hom-associative algebra Hom-Lie algebra Kegel's theorem.
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| Fund Project:Supported by the Excellent Young Talents Fund Project of Anhui Province (Grant No.2013SQRL092ZD), the Natural Science Foundation of Anhui Province (Grant Nos.1408085QA06; 1408085QA08), the Excellent Young Talents Fund Project of Chuzhou University (Grant No.2013RC001) and the Research and Innovation Project for College Graduates of Jiangsu Province (Grant No.CXLX12-0071). |
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| Abstract: |
| Let $A$ be a multiplicative Hom-associative algebra and $L$ a multiplicative Hom-Lie algebra together with surjective twisting maps. We show that if $A$ is a sum of two commutative Hom-associative subalgebras, then the commutator Hom-ideal is nilpotent. Furthermore, we obtain an analogous result for Hom-Lie algebra $L$ extending Kegel's Theorem. Finally, we discuss the Hom-Lie ideal structure of a simple Hom-associative algebra $A$ by showing that any non-commutative Hom-Lie ideal of $A$ must contain $[A,A].$ |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2014.04.008 |
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