131
Views
3
CrossRef citations to date
0
Altmetric
Original Articles

Free Rota-Baxter systems and a Hopf algebra structure

&
Pages 3913-3925 | Received 15 Aug 2017, Published online: 26 Feb 2018

References

  • Abe, E. (1980). Hopf Algebras. Cambridge: Cambridge University Press.
  • Adams, W. W., Loustaunau, P. (1994). An introduction to Gröbner bases. Graduate Studies in Mathematics, Vol. 3. Providence: American Mathematical Society.
  • Baxter, G. (1960). An analytic problem whose solution follows from a simple algebraic identity. Pacific J. Math. 10:731–742.
  • Bergman, G. M. (1978). The diamond lemma for ring theory. Adv. Math. 29:178–218.
  • Bokut, L. A. (1976). Imbeddings into simple associative algebras. Algebra i Logika 15:117–142.
  • Bokut, L. A., Chen, Y. Q. (2014). Gröbner-Shirshov bases and their calculation. Bull. Math. Sci. 4:325–395.
  • Bokut, L. A., Chen, Y. Q., Qiu, J. J. (2010). Gröbner-Shirshov bases for associative algebras with multiple operations and free Rota-Baxter algebras. J. Pure Appl. Alg. 214:89–100.
  • Bokut, L. A., Kolesnikov, P. S. (2003). Gröbner-Shirshov bases: from their incipiency to the present. J. Math. Sci. 116(1):2894–2916.
  • Bokut, L. A., Kukin, G. (1994). Algorithmic and Combinatorial Algebra. Dordrecht: Kluwer Academic Publ.
  • Brzeziński, T. (2016). Rota-Baxter systems, dendriform algebras and covariant bialgebras. J. Algebra 460(15):1–25.
  • Buchberger, B. (1970). An algorithmical criteria for the solvability of algebraic systems of equations. Aequat. Math. 4:374–383.
  • Buchberger, B., Winkler, F. (1998). Gröbner bases and applications. London Mathematical Society Lecture Note Series, Vol. 251. Cambridge: Cambridge University Press.
  • Cartier, P. (1972). On the structure of free Baxter algebras. Adv. Math. 9:253–265.
  • Connes, A., Kreimer, D. (1998). Hopf algebras, renormalization and non-commutative geometry. Commun. Math. Phys. 199:203–242.
  • Ebrahimi-Fard, K., Guo, L. (2006). Quasi-shuffles, mixable shuffles and Hopf algebras. J. Algebr. Comb. 24:83–101.
  • Ebrahimi-Fard, K., Guo, L. (2008). Rota-Baxter algebras and dendriform dialgebras. J. Pure Appl. Alg. 212:320–339.
  • Ebrahimi-Fard, K., Guo, L. (2008). Free Rota-Baxter algebras and rooted trees. J. Alg. Appl. 7:167–194.
  • Gao, X., Guo, L., Zhang, T. (2016). Bialgebra and Hopf algebra structures on free Rota-Baxter algebras. arXiv:1604.03238 [math.RA].
  • Guo, L. (2012). An Introduction to Rota-Baxter Algebra. Beijing: Higher Education Press.
  • Guo, L., Keigher, W. (2000). Baxter algebras and Shuffle products. Adv. Math. 150:117–149.
  • Guo, L., Keigher, W. (2000). On free Baxter algebras: completions and the internal construction. Adv. Math. 151: 101–127.
  • Guo, L., Sit, W., Zhang, R. (2013). Differential type operators and Gröbner-Shirshov bases. J. Symbolic Comput. 52: 97–123.
  • Hironaka, H. (1964). Resolution of singulatities of an algebtaic variety over a field if characteristic zero, I, II. Ann. Math. 79:109–203, 205–326.
  • Loday, J. L., Ronco, M. O. (2004). Trialgebras and families of polytopes, in Homotopy Theory: Relations with algebraic Geometry, Group Cohomology, and Algebraic K-theory. Contemp. Math. 346:369–398.
  • Rota, G. C. (1969). Baxter algebras and combinatorial identities I. Bull. Amer. Math. Soc. 5:325–329.
  • Shirshov, A. I. (1962). Some algorithmic problem for Lie algebras, Sibirsk. Mat. Z. 3:292–296.
  • Zhang, T., Gao, X., Guo, L. (2016). Hopf algebras of rooted forests, cocyles and free Rota-Baxter algebras. J. Math. Phys. 57:101701.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.