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Rank of quantized universal enveloping algebras and modular functions

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Abstract

We compute an intrinsic rank invariant for quasitriangular Hopf algebras in the case of general quantum groupsU q (g). As a function ofq the rank has remarkable number theoretic properties connected with modular covariance and Galois theory. A number of examples are treated in detail, including rank (U q (su(3))) and rank (U q (e 8)). We briefly indicate a physical interpretation as relating Chern-Simons theory with the theory of a quantum particle confined to an alcove ofg.

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Author notes

  1. Shahn Majid (SERC Research Fellow and Drapers Fellow)

    Present address: Pembroke College, Cambridge

Authors and Affiliations

  1. Department of Applied Mathematics and Theoretical Physics, University of Cambridge, CB3 9EW, Cambridge, UK

    Shahn Majid (SERC Research Fellow and Drapers Fellow)

  2. Computer Centre, University of Rostov, Rostov-on-Don, USSR

    Ya. S. Soibelman

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  1. Shahn Majid
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  2. Ya. S. Soibelman
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Communicated by N. Yu. Reshetikhin

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Majid, S., Soibelman, Y.S. Rank of quantized universal enveloping algebras and modular functions. Commun.Math. Phys. 137, 249–262 (1991). https://doi.org/10.1007/BF02431880

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  • DOI: https://doi.org/10.1007/BF02431880

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