On the Associative Nijenhuis Relation

We give the construction of a free commutative unital associative Nijenhuis algebra on a commutative unital associative algebra based on an augmented modified quasi-shuffle product.

[1]  Maria O. Ronco.  Eulerian idempotents and Milnor–Moore theorem for certain non-cocommutative Hopf algebras , 2002 .

[2]  Li Guo,et al.  QUASI-SHUFFLES , MIXABLE SHUFFLES AND HOPF ALGEBRAS , 2004 .

[3]  F. Atkinson,et al.  Some aspects of Baxter's functional equation , 1963 .

[4]  Jean-Louis Loday,et al.  Trialgebras and families of polytopes , 2002 .

[5]  Frédéric Chapoton,et al.  Dialgebras and Related Operads , 2001 .

[6]  Joseph P. S. Kung,et al.  Gian-Carlo Rota on combinatorics : introductory papers and commentaries , 1995 .

[7]  A. Belavin,et al.  Triangle Equations and Simple Lie Algebras , 1998 .

[8]  P. J. Higgins.  UNIVERSAL ALGEBRA: (Mathematics and its Applications, 6) , 1982 .

[9]  Li Guo.  BAXTER ALGEBRAS AND DIFFERENTIAL ALGEBRAS , 2002 .

[10]  V. Sokolov,et al.  One More Kind of the Classical Yang-Baxter Equation , 2000 .

[11]  Gian-Carlo Rota,et al.  Ten Mathematics Problems I will never solve , 1998 .

[12]  Vladimir V. Sokolov,et al.  Generalized Operator Yang-Baxter Equations, Integrable ODEs and Nonassociative Algebras , 2000 .

[13]  L. Chau,et al.  Differential Geometric Methods in Theoretical Physics , 1990 .

[14]  G. Baxter,et al.  AN ANALYTIC PROBLEM WHOSE SOLUTION FOLLOWS FROM A SIMPLE ALGEBRAIC IDENTITY , 1960 .

[15]  Franco Magri,et al.  Poisson-Nijenhuis structures , 1990 .

[16]  Quantum Bi-Hamiltonian Systems , 2000, math-ph/0610011.

[17]  Maria O. Ronco,et al.  Primitive elements in a free dendriform algebra , 1999 .

[18]  D. Kreimer.  Structures in Feynman Graphs -Hopf Algebras and Symmetries , 2002, hep-th/0202110.

[19]  Pierre Cartier,et al.  On the structure of free baxter algebras , 1972 .

[20]  New mathematical structures in renormalizable quantum field theories , 2002, hep-th/0211136.

[21]  Li Guo,et al.  Baxter Algebras and Shuffle Products , 2000 .

[22]  Desmond Fearnley-Sander,et al.  Universal Algebra , 1982 .

[23]  Philippe Leroux,et al.  Construction of Nijenhuis operators and dendriform trialgebras , 2004, Int. J. Math. Math. Sci..

[24]  K. Ebrahimi-Fard.  Loday-Type Algebras and the Rota–Baxter Relation , 2002 .

[25]  Michael E. Hoffman,et al.  Quasi-Shuffle Products , 1999 .

[26]  George Gratzer,et al.  Universal Algebra , 1979 .

[27]  Gian-Carlo Rota,et al.  Baxter algebras and combinatorial identities. II , 1969 .