On Frobenius algebras and the quantum YangBaxter equation
Authors:
K. I. Beidar, Y. Fong and A. Stolin
Journal:
Trans. Amer. Math. Soc. 349 (1997), 38233836
MSC (1991):
Primary 81R50; Secondary 16L60
MathSciNet review:
1401512
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Abstract: It is shown that every Frobenius algebra over a commutative ring determines a class of solutions of the quantum YangBaxter equation, which forms a subbimodule of its tensor square. Moreover, this subbimodule is free of rank one as a left (right) submodule. An explicit form of a generator is given in terms of the Frobenius homomorphism. It turns out that the generator is invertible in the tensor square if and only if the algebra is Azumaya.
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Additional Information
K. I. Beidar
Affiliation:
Department of Mathematics, National ChengKung University, Tainan, Taiwan
Email:
beidar@mail.ncku.edu.tw; fong@mail.ncku.edu.tw
A. Stolin
Affiliation:
Department of Mathematics, University of Göteborg, S41296 Göteborg, Sweden
Email:
astolin@math.chalmers.se
DOI:
http://dx.doi.org/10.1090/S0002994797018084
PII:
S 00029947(97)018084
Keywords:
Quantum YangBaxter equation,
Frobenius algebra,
Azumaya algebra.
Received by editor(s):
August 4, 1995
Received by editor(s) in revised form:
March 7, 1996
Additional Notes:
We would like to express our gratitude to the Swedish Academy of Science for the support of the visit of the first author to Sweden, during which this paper was finished. We are thankful to Professor B. Pareigis for fruitful discussions.
Article copyright:
© Copyright 1997
American Mathematical Society
