Manin Triples and Bialgebras of Left-Alia Algebras Associated with Invariant Theory - Chuangchuang Kang; Guilai Liu; Zhuo Wang; Shizhuo Yu (Mathematics, 2024)
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.