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Totally compatible associative and Lie dialgebras,tridendriform algebras and PostLie algebras

Totally compatible associative and Lie dialgebras,tridendriform algebras and PostLie algebras
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摘要 This paper studies the concepts of a totally compatible dialgebra and a totally compatible Lie dialgebra,defined to be a vector space with two binary operations that satisfy individual and mixed associativity conditions and Lie algebra conditions respectively.We show that totally compatible dialgebras are closely related to bimodule algebras and semi-homomorphisms.More significantly,Rota-Baxter operators on totally compatible dialgebras provide a uniform framework to generalize known results that Rota-Baxter related operators give tridendriform algebras.Free totally compatible dialgebras are constructed.We also show that a Rota-Baxter operator on a totally compatible Lie dialgebra gives rise to a PostLie algebra,generalizing the fact that a Rota-Baxter operator on a Lie algebra gives rise to a PostLie algebra. This paper studies the concepts of a totally compatible dialgebra and a totally compatible Lie dialgebra,defined to be a vector space with two binary operations that satisfy individual and mixed associativity conditions and Lie algebra conditions respectively.We show that totally compatible dialgebras are closely related to bimodule algebras and semi-homomorphisms.More significantly,Rota-Baxter operators on totally compatible dialgebras provide a uniform framework to generalize known results that Rota-Baxter related operators give tridendriform algebras.Free totally compatible dialgebras are constructed.We also show that a Rota-Baxter operator on a totally compatible Lie dialgebra gives rise to a PostLie algebra,generalizing the fact that a Rota-Baxter operator on a Lie algebra gives rise to a PostLie algebra.
出处 《Science China Mathematics》 SCIE 2014年第2期259-273,共15页 中国科学:数学(英文版)
基金 supported by National Natural Science Foundation of China(Grant Nos.10920161,11271202,11221091 and 11371178) Specialized Research Fund for the Doctoral Program of Higher Education(Grant Nos.200800550015 and 20120031110022) National Science Foundation of USA(Grant No.DMS-1001855)
关键词 totally compatible algebra Rota-Baxter operator tridendriform algebra PostLie algebra Lie代数 Post 全兼容 代数和 联想 运营商 向量空间 二元运算
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  • 1Aguiar M. Infinitesimal Hopf algebras. Contemp Math, 2000, 267: 1-29.
  • 2Bai C. Double constructions of Frobenius algebras, Connes cocycles and their duality. J Noncommut Geom, 2010, 4: 476-530.
  • 3Bai C, Guo L, Ni X. Relative Rota-Baxter algebras and tridendriform algebras. J Algebra Appl, 2013, 12: 1350027.
  • 4Bai C, Guo L, Ni X. Nonabelian generalized Lax pairs, the classical Yang-Baxter equation and Post Lie algebras. Commun Math Phys, 2010, 297: 553-596.
  • 5Bai C, Guo L, Ni X. O-operators on associative algebras, associative Yang-Baxter equations and dendriform algebras. In: Quantized Algeba and Physics. Singapore: World Scientific, 2011, 10-51.
  • 6Baxter G. An analytic problem whose solution follows from a simple algebraic identity. Pacific J Math, 1969, 10: 731-742.
  • 7Chen Y, Mo Q. Embedding dendriform dialgebra into its universal enveloping Rota-Baxter algebra. Proc Amer Math Soc, 2011, 139: 4207-4216.
  • 8Dotsenko V. Compatible associative products and trees. Algebra Number Theory, 2009, 3: 567-586.
  • 9Dotsenko V V, Khoroshkin A S. Character formulas for the operad of a pair of compatible brackets and for the bi-Hamiltonian operad. Funct Anal Appl, 2007, 41: 1-7.
  • 10Ebrahimi-Fard E. Loday-type algebras and the Rota-Baxter relation. Lett Math Phys, 2002, 61: 139-147.

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