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arXiv · 2403.05339

Manin triples and bialgebras of Left-Alia algebras associated to invariant theory

Kang Chuangchuang·Liu Guilai·Wang Zhuo·Yu Shizhuo
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Abstract

A left-Alia algebra is a vector space together with a bilinear map satisfying symmetric Jocobi identity. Motivated by invariant theory, we first construct a class of left-Alia algebras induced by twisted derivations. Then, we introduce the notion of Manin triples and bialgebras of left-Alia algebras. Via specific matched pairs of left-Alia algebras, we figure out the equivalence between Manin triples and bialgebras of left-Alia algebras.

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Kang Chuangchuang, Liu Guilai, Wang Zhuo, Yu Shizhuo. 2024-03-08. Manin triples and bialgebras of Left-Alia algebras associated to invariant theory. https://arxiv.org/abs/2403.05339

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