Chengming Bai

Splitting of Operations, Manin Products, and Rota–Baxter Operators

This paper provides a general operadic definition for the notion of splitting the operations of algebraic structures. This construction is proved to be equivalent to some Manin products of operads in the case of quadratic operads and it is shown to be closely related to Rota–Baxter operators. Hence, it gives a new effective way to compute Manin black products. Finally, this allows us to describe the algebraic structure of square matrices with coefficients in algebras of certain types. Many examples illustrate this text, including an example of nonquadratic algebras with Jordan algebras.

Nonabelian Generalized Lax Pairs, the Classical Yang-Baxter Equation and PostLie Algebras

We generalize the classical study of (generalized) Lax pairs, the related

Some results on L-dendriform algebras

{\mathcal O}

A Lie algebraic approach to Novikov algebras

-operators and the (modified) classical Yang-Baxter equation by introducing the concepts of nonabelian generalized Lax pairs, extended

Realizations of conformal current-type Lie algebras

{\mathcal O}

A Hom-version of the affinizations of Balinskii–Novikov and Novikov superalgebras

-operators and the extended classical Yang-Baxter equation. We study in this context the nonabelian generalized r-matrix ansatz and the related double Lie algebra structures. Relationship between extended