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

Chengming Bai, Olivia Bellier, Li Guo, Xiang Ni
2012 International mathematics research notices  
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 and it is shown to be closely related to Rota-Baxter operators. Hence, it gives a new effective way to compute Manin black products. The present construction is shown to have symmetry properties. Finally, this allows us to describe the algebraic structure of square matrices with coefficients in
more » ... fficients in algebras of certain types. Many examples illustrate this text, including the case of Jordan algebras.
doi:10.1093/imrn/rnr266 fatcat:kjbgdhmglreudaw7t66tasdi4y