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Regular solutions of quantum Yang-Baxter equation from weak hopf algebras

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Czechoslovak Journal of Physics Aims and scope

Abstract

Generalization of Hopf algebraslq (2) by weakening the invertibility of the generatorK, i.e., exchanging its invertibilityKK −1=1 to the regularity K\(\bar K\)K=K is studied. Two weak Hopf algebras are introduced: a weak Hopf algebrawslq (2) and aJ-weak Hopf algebravslq (2) which are investigated in detail. The monoids of group-like elements ofwslq (2) andvslq (2) are regular monoids, which supports the general conjucture on the connection betweek weak Hopf algebras and regular monoids. A quasi-braided weak Hopf algebraŪqw is constructed fromwslq (2). It is shown that the corresponding quasi-R-matrix is regular Rw \(\hat R\) wRw=Rw.

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Authors and Affiliations

  1. Theory Group, Nuclear Physics Laboratory, Kharkov National University, 61077, Kharkov, Ukraine

    Steven Duplij

  2. Department of Mathematics, Zhejiang University (Xixi Campus), 310028, Hangzhou, Zhejiang, China

    Fang Li

Authors
  1. Steven Duplij
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  2. Fang Li
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Project (No. 19971074) supported by the National Natural Science Foundation of China.

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Duplij, S., Li, F. Regular solutions of quantum Yang-Baxter equation from weak hopf algebras. Czech J Phys 51, 1306–1311 (2001). https://doi.org/10.1023/A:1013313802053

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  • DOI: https://doi.org/10.1023/A:1013313802053

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