ROTA-BAXTER CATEGORIES

Year 2009, Volume: 5 Issue: 5, 27 - 57, 01.06.2009

Edmundo Castillo Rafael Diaz

Abstract

We introduce Rota-Baxter categories and construct examples of such structures.

Keywords

Rota-Baxter algebras, categorification of rings, categorical integration

References

• M. Aguiar and W. Moreira, Combinatorics of the free Baxter algebra, Electron. J. Combin., 13 (2006), R17.
• J. Baez and J. Dolan, From finite set to Feynman diagrams, in Bj¨orn En- gquist and Wilfried Schmid (Eds.), Mathematics Unlimited - 2001 and Beyond, Springer, Berlin, 2001, pp. 29-50.
• J. Baez and J. Dolan, Categorification, in E. Getzler, M. Kapranov (Eds.), Higher category theory, Evanston, IL, 1997, Contemp. Math., vol. 230, Amer.
• Math. Soc., Providence, RI, 1998, pp. 1-36.
• F. Bergeron, G. Labelle and P. Leroux, Combinatorial species and tree-like structures, Cambridge Univ. Press, Cambridge, 1998.
• H. Bland´ın and R. D´ıaz, Compositional Bernoulli numbers, Afr. Diaspora J. Math, at press. H. Bland´ın and R. D´ıaz, On the combinatorics of hypergeometric functions, Adv. Stud. Contemp. Math, 14 (2007), 153-160.
• H. Bland´ın and R. D´ıaz, Rational combinatorics, Adv. in Appl. Math., 40 (2008), 107-126.
• E. Castillo and R. D´ıaz, Categorical renormalization, in preparation. P. Cartier, On the structure of Baxter algebras, Adv. in Math., 9 (1972), 253
• L. Crane and I. Frenkel, Four-dimensional topological quantum field theory, Hopf categories, and the canonical bases, J. Math. Phys., 35 (1994), 5136-5154.
• L. Crane and D. Yetter, Examples of categorification, Gahiers Topologie G´eom. Deff´erentielle Cat´eg., 39 (1998), 3-25.
• P. Cheung and V. Kac, Quantum Calculus, Springer-Verlag, Berlin, 2002.
• A. Connes and D. Kreimer, Renormalization in quantum field theory and Riemann-Hilbert problem I, Comm. Math. Phys., 210 (2000), 249-273.
• R. D´ıaz and E. Pariguan, Categorification of Feynman Integrals, in prepara- tion. R. D´ıaz and E. Pariguan, Feynman-Jackson integrals, J. Nonlinear Math. Phys., 13 (2006), 365-376.
• R. D´ıaz and E. Pariguan, An example of Feynman-Jackson integral, J. Phys. A, 40 (2007), 1265-1272.
• R. D´ıaz and E. Pariguan, Super, quantum and noncommutative species, preprint, arXiv:math.CT/0509674.
• R. D´ıaz and M. P´aez, On an identity in Rota-Baxter algebras, Sm. Lothar. Combin. 57 (2007), B57b.
• R. D´ıaz and C. Teruel, q, k-generalized gamma and beta functions, J. Nonlinear Math. Phys., 12 (2005), 118-134.
• K. Ebraihimi-Fard and L. Guo, On free Rota-Baxter algebras, preprint, arXiv:math.NT/0510266.
• M. Goresky and R. MacPherson, Intersection homology, Topology, 19 (1980), 162.
• A. Joyal, Une th´eorie combinatoire des s´eries formelles, Adv. in Math., 42 (1981), 1-82.
• M. Laplaza, Coherence for distributivity, in Coherence in Categories, Lecture Notes in Math., vol. 281, Springer, Berlin, 1972, pp. 29-65.
• M. Khovanov, A categorification of Jones polynomial, Duke Math. J., 143 (1986), 288-348.
• S. Mac Lane, Categories for the Working Mathematician, Springer, Berlin and New York, 1971.
• G. C. Rota, Gian-Carlo Rota on Combinatorics, Joseph Kung (Ed.), Birkh¨auser, Boston and Basel, 1995. Edmundo Castillo
• Facultad de Ciencias Universidad Central de Venezuela Caracas 1020, Venezuela e-mail: [e-mail] Rafael D´ıaz
• Facultad de Administraci´on Universidad del Rosario Bogota, Colombia e-mail: [e-mail]