Splitting of operations, Manin products and Rota-Baxter operators

Details Splitting of operations, Manin products and Rota-Baxter operators Splitting of operations, Manin products and Rota-Baxter operators

2011-06-29

arxiv.org/abs/1106.6080v1

Mathematics

Quantum Algebra

33 pages

Scientific paper

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 algebras of certain types. Many examples illustrate this text, including the case of Jordan algebras.

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