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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Solutions to the quantum Yang-Baxter equation arising from pointed bialgebras
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by David E. Radford PDF
Trans. Amer. Math. Soc. 343 (1994), 455-477 Request permission

Abstract:

Let $R:M \otimes M \to M \otimes M$ be a solution to the quantum Yang-Baxter equation, where M is a finite-dimensional vector space over a field k. We introduce a quotient ${A^{{\text {red}}}}(R)$ of the bialgebra $A(R)$ constructed by Fadeev, Reshetihkin and Takhtajan, whose characteristics seem to more faithfully reflect properties R possesses as a linear operator. We characterize all R such that ${A^{{\text {red}}}}(R)$ is a pointed bialgebra, and we determine all solutions R to the quantum Yang-Baxter equation when ${A^{{\text {red}}}}(R)$ is pointed and $\dim M = 2$ (with a few technical exceptions when k has characteristic 2). Extensions of such solutions to the quantum plane are studied.
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Additional Information
  • © Copyright 1994 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 343 (1994), 455-477
  • MSC: Primary 17B37; Secondary 16W30
  • DOI: https://doi.org/10.1090/S0002-9947-1994-1201324-2
  • MathSciNet review: 1201324