International Mathematics Research Notices· 2012Q1
Splitting of Operations, Manin Products, and Rota–Baxter Operators
- 186citations
- Q1SCImago
- 2012year
Short summary
A new general operadic definition for splitting algebraic operations is introduced, shown to be equivalent to Manin products of operads for quadratic operads and related to Rota–Baxter operators.
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Key points
- Introduces a general operadic definition for splitting operations of algebraic structures.
- Demonstrates equivalence between this splitting construction and Manin products of operads for quadratic operads.
- Establishes a close relationship between splitting operations and Rota–Baxter operators.
- Provides a new method for computing Manin products and describes algebraic structures of square matrices.
AI-generated from the title and abstract; the full text is not read.
Abstract
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.
The authors' abstract, as published at the source. International Mathematics Research Notices, 2012 · DOI ↗
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Field: Algebra and Number Theory
Algebra and Number TheoryMathematics