Loday-type algebras and the Rota-Baxter relation

Letters in Mathematical Physics

Volumn 61, Issue 2, 2002, Pages 139-147

  Ebrahimi Fard, K ^a  

^a UNIVERSITY OF BONN   (Germany)

Author keywords

Associative classical Yang Baxter equation; Classical Yang Baxter equation; Dendriform di trialgebras; Minimal subtraction scheme; Rota Baxter relation

Indexed keywords

EID: 0041314056     PISSN: 03779017     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1020712215075     Document Type: Article

References (20)

1. Rota, G.-C.: Ten mathematics problems I will never solve. Mitt. Dtsch. Math.-Ver. No. 2 (1998), 45-52.
2. Guo, L. and Keigher. W.: Baxter algebras and shuffle products. Adv. Math. 150(1) (2000), 117-149.
3. Baxter, G.: An analytic problem whose solution follows from a simple algebraic identity. Pacific J. Math. 10 (1960), 731-742.
4. Atkinson, F. V.: Some aspects of Baxter's functional equation, J. Math. Anal. Appl. 7 (1963), 1-30.
5. Miller, J. B.: Baxter operators and endomorphisms on Banach algebras, J. Math. Anal. Appl. 25 (1969), 503-520.
6. Rota, G.-C.: Baxter operators, an introduction. In: Gian-Carlo Rota on Combinatorics, Contemp. Mathematicians. Birkhäuser, Boston, 1995, pp. 504-512.
7. Rota, G.-C.: Baxter algebras and combinatorial identities. I, II., Bull. Amer. Math. Soc. 75 (1969), 325-329; ibid. 75 (1969), 330-334.
8. Rota, G.-C.: Baxter algebras and combinatorial identities. I, II., Bull. Amer. Math. Soc. 75 (1969), 325-329; ibid. 75 (1969), 330-334.
9. Cartier, P.: On the structure of free Baxter algebras, Adv. Math. 9 (1972), 253-265.
10. Connes, A. and Kreimer, D.: Renormalization in quantum field theory and the Riemann-Hilbert problem. I. The Hopf algebra structure of graphs and the main theorem, Comm. Math. Phys. 210 (1) (2000), 249-273.
11. Connes, A. and Kreimer, D.: Renormalization in quantum field theory and the Riemann-Hilbert problem. II. The β-function, diffeomorphisms and the renormalization group, Comm. Math. Phys. 216(1) (2001), 215-241.
12. Loday, J.-L.: Dialgebras, In: Dia/gebras and Related Operads, Lecture Notes in Math. 1763, Springer, New York, 2001, pp. 7-66.
13. Loday, J.-L. and Ronco, M.: Trialgebras and families of polytopes, Preprint, math AT/ 0205043, mai 2002.
14. Aguiar, M.: Pre-Poisson algebras, Lett. Math. Phys. 54(4) (2000), 263-277.
15. Aguiar, M.: On the associative analog of Lie bialgebras, J. Algebra 244 (2001), 492-532.
16. Semenov-Tian-Shansky, M. A.: What is a classical r-matrix? Funct. Anal. Appl. 17 (1983), 259-272; (Russian) Funktsional. Anal, i Prilozhen. 17(4) (1983), 17-33.
17. Semenov-Tian-Shansky, M. A.: What is a classical r-matrix? Funct. Anal. Appl. 17 (1983), 259-272; (Russian) Funktsional. Anal, i Prilozhen. 17(4) (1983), 17-33.
18. Belavin, A. A. and Drinfeld, V. G.: Triangle Equations and Simple Lie Algebras, Class. Rev. Math. Math. Phys. 1, Harwood Acad. Publ. Amsterdam, 1998.
19. Ebrahimi-Fard, K.: From Baxter to Baxter, In preparation.
20. Kreimer, D.: On the Hopf algebra structure of perturbative quantum field theories. Adv. Theor. Math. Phys. 2 (1998), 303-334.