Hom–Novikov algebras
Hom–Novikov algebras
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DOI：
10.1088/1751-8113/44/8/085202
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发表时间：
2009-09
期刊：
影响因子：
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通讯作者：
Donald Yau
中科院分区：
文献类型：
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作者：
Donald Yau
我们研究了Novikov代数的一个扭曲推广，称为Hom-Novikov代数，其中两个定义恒等式被一个线性映射扭曲。证明了通过沿着任意代数自同态扭曲，可以从Novikov代数得到Hom-Novikov代数.计算了2维或3维复Novikov代数上的所有代数自同态，并明确地描述了它们的Hom-Novikov代数.另一类Hom-Novikov代数是由Hom-commutative代数和一个导子构造而成的，推广了Dorfman和Gel'fand的一个构造。另外两类Hom-Novikov代数是由Hom-Lie代数和一个合适的线性自同态构造的，推广了Bai和Meng的一个构造。
We study a twisted generalization of Novikov algebras, called Hom–Novikov algebras, in which the two defining identities are twisted by a linear map. It is shown that Hom–Novikov algebras can be obtained from Novikov algebras by twisting along any algebra endomorphism. All algebra endomorphisms on complex Novikov algebras of dimensions 2 or 3 are computed, and their associated Hom–Novikov algebras are described explicitly. Another class of Hom–Novikov algebras is constructed from Hom-commutative algebras together with a derivation, generalizing a construction due to Dorfman and Gel'fand. Two other classes of Hom–Novikov algebras are constructed from Hom–Lie algebras together with a suitable linear endomorphism, generalizing a construction due to Bai and Meng.