Manin Triples and Bialgebras of Left-Alia Algebras Associated with Invariant Theory

Chuangchuang Kang, Guilai Liu (), Zhuo Wang and Shizhuo Yu
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Chuangchuang Kang: School of Mathematical Sciences, Zhejiang Normal University, Jinhua 321004, China
Guilai Liu: Chern Institute of Mathematics and LPMC, Nankai University, Tianjin 300071, China
Zhuo Wang: School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300317, China
Shizhuo Yu: School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300317, China

Mathematics, 2024, vol. 12, issue 3, 1-16

Abstract: A left-Alia algebra is a vector space together with a bilinear map satisfying the symmetric Jacobi identity. Motivated by invariant theory, we first construct a class of left-Alia algebras induced by twisted derivations. Then, we introduce the notions 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.

Keywords: left-Alia algebra; bialgebra; invariant theory; Manin triple; matched pair; representation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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