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Baxter algebras and Hopf algebras
Author(s):
George
E.
Andrews;
Li
Guo;
William
Keigher;
Ken
Ono
Journal:
Trans. Amer. Math. Soc.
355
(2003),
4639-4656.
MSC (2000):
Primary 16W30, 16W99
Posted:
May 15, 2003
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Additional information
Abstract:
By applying a recent construction of free Baxter algebras, we obtain a new class of Hopf algebras that generalizes the classical divided power Hopf algebra. We also study conditions under which these Hopf algebras are isomorphic.
References:
- 1.
- G. Baxter, An analytic problem whose solution follows from a simple algebraic identity, Pacific J. Math. 10 (1960), 731-742. MR 22:9990
- 2.
- P. Berthelot and A. Ogus, Notes on Crystalline Cohomology, Princeton University Press, Princeton, NJ, 1978. MR 58:10908
- 3.
- P. Cartier, On the structure of free Baxter algebras, Adv. in Math. 9 (1972), 253-265. MR 49:2807
- 4.
- K.-T. Chen, Integration of paths, geometric invariants and a generalized Baker-Hausdorff formula, Ann. of Math. 65 (1957), 163-178. MR 19:12a
- 5.
- L. Guo, Properties of free Baxter algebras, Adv. in Math. 151 (2000), 346-374. MR 2001f:16048
- 6.
- L. Guo, Baxter algebras and the umbral calculus, Adv. in Appl. Math. 27 (2001), 405-426. MR 2003b:05020
- 7.
- L. Guo, Baxter algebras and differential algebras, In: Differential Algebra and Related Topics, World Scientific Publishing, River Edge, NJ, 2002, pp. 281-305.
- 8.
- L. Guo and W. Keigher, Baxter algebras and shuffle products, Adv. in Math. 150 (2000), 117-149. MR 2001g:05015
- 9.
- L. Guo and W. Keigher, On free Baxter algebras: completions and the internal construction, Adv. in Math. 151 (2000), 101-127. MR 2001c:16046
- 10.
- W. Keigher, On the ring of Hurwitz series, Comm. Algebra 25 (1997), 1845-1859. MR 98e:13022
- 11.
- H. Matsumura, Commutative Ring Theory, Cambridge University Press, 1994. MR 90i:13001
- 12.
- W. Nichols and M. Sweedler, Hopf algebras and combinatorics, In: Umbral Calculus and Hopf Algebras, Contemporary Mathematics 6, Amer. Math. Soc., Providence, RI, 1982, pp. 49-84. MR 83g:16019
- 13.
- R. Ree, Lie elements and an algebra associated with shuffles, Ann. Math. 68 (1958), 210-220. MR 26:6447
- 14.
- J. Riordan, Combinatorial Identities, John Wiley and Sons, New York, 1968. MR 38:53
- 15.
- S. Roman, The Umbral Calculus, Pure and Applied Mathematics 111, Academic Press, Orlando, FL, 1984. MR 87c:05015
- 16.
- S. Roman and G.-C. Rota, The umbral calculus, Adv. Math. 27 (1978), 95-188. MR 58:5256
- 17.
- G.-C. Rota, Baxter algebras and combinatorial identities. I, II, Bull. Amer. Math. Soc. 75 (1969), 325-329, 330-334. MR 39:5387
- 18.
- G.-C. Rota, Baxter operators, an introduction, In: Gian-Carlo Rota on Combinatorics, Introductory Papers and Commentaries, Joseph P. S. Kung, editor, Birkhäuser, Boston, 1995, pp. 504-512. MR 99b:01027
- 19.
- G.-C. Rota, Ten mathematics problems I will never solve, Invited address at the joint meeting of the American Mathematical Society and the Mexican Mathematical Society, Oaxaca, Mexico, December 6, 1997, Mitt. Dtsch. Math.-Ver., Heft 2, 1998, pp. 45-52.
- 20.
- D. Stanton and D. White, Constructive Combinatorics, Springer-Verlag, New York, 1986. MR 88a:05001
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Additional Information:
George
E.
Andrews
Affiliation:
Department of Mathematics, Pennsylvania State University, University Park, Pennsylvania 16802
Email:
andrews@math.psu.edu
Li
Guo
Affiliation:
Department of Mathematics and Computer Science, Rutgers University at Newark, Newark, New Jersey 07102
Email:
liguo@newark.rutgers.edu
William
Keigher
Affiliation:
Department of Mathematics and Computer Science, Rutgers University at Newark, Newark, New Jersey 07102
Email:
keigher@newark.rutgers.edu
Ken
Ono
Affiliation:
Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
Email:
ono@math.wisc.edu
DOI:
10.1090/S0002-9947-03-03326-9
PII:
S 0002-9947(03)03326-9
Keywords:
Free Baxter algebra,
Hopf algebra,
divided power
Received by editor(s):
January 24, 2003
Posted:
May 15, 2003
Additional Notes:
The first and fourth authors are supported by grants from the National Science Foundation, and the fourth author is supported by Alfred P. Sloan, David and Lucile Packard, and H. I. Romnes Fellowships.
Copyright of article:
Copyright
2003,
American Mathematical Society
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