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The Pentagon equation and mapping-class groups of punctured surfaces

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Abstract

In the quantum Teichmüller theory, the mapping-class groups of punctured surfaces are represented projectively based on Penner coordinates. Algebraically, the representation is based on the pentagon equation together with pair of additional relations. Two more examples of solutions of these equations are connected with matrix (or operator) generalizations of the Rogers dilogarithm. The corresponding central charges are rational. It is possible that this system of equations admits many different solutions.

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Authors and Affiliations

  1. Steklov Mathematical Institute, St. Petersburg, Russia

    R. M. Kashaev

  2. Helsinki Institute of Physics, University of Helsinki, Finland

    R. M. Kashaev

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  1. R. M. Kashaev
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 123, No. 2, pp. 198–204, May, 2000.

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Kashaev, R.M. The Pentagon equation and mapping-class groups of punctured surfaces. Theor Math Phys 123, 576–581 (2000). https://doi.org/10.1007/BF02551393

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  • DOI: https://doi.org/10.1007/BF02551393

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