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

Bai, Chengming and Bellier, Olivia and Guo, Li and Ni, Xiang (2013) Splitting of Operations, Manin Products, and Rota–Baxter Operators. International Mathematics Research Notices, 2013 (3). pp. 485-524. ISSN 1073-7928.

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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.

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Additional Information:© 2012 The Authors(s). Published by Oxford University Press. Received December 6, 2011; Accepted December 12, 2011. Advance Access Publication January 22, 2012. Communicated by Prof. Andrei Zelevinsky. O.B. is grateful to thank the Max-Planck Institute for Mathematics for the excellent working conditions she enjoyed there. The authors thank Bruno Vallette for his many helps, and the Chern Institute of Mathematics at Nankai University and the CNRS on the occasion of “l’action francochinoise de mathématiques" for providing a stimulating environment that fostered this collaboration during the Sino-France Summer Workshop on Operads and Universal Algebra in June-July 2010. C.B. acknowledges the support by NSFC (10920161) and SRFDP (200800550015). L.G. thanks NSF grant DMS-1001855 for support.
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Issue or Number:3
Record Number:CaltechAUTHORS:20130329-082553594
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Official Citation: Chengming Bai, Olivia Bellier, Li Guo, and Xiang Ni Splitting of Operations, Manin Products, and Rota–Baxter Operators Int Math Res Notices (2013) Vol. 2013 485-524 first published online January 22, 2012 doi:10.1093/imrn/rnr266
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:37682
Deposited By: Tony Diaz
Deposited On:16 Apr 2013 21:46
Last Modified:03 Oct 2019 04:50

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