Rank of quantized universal enveloping algebras and modular functions |
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| Authors: | Shahn Majid Ya S Soibelman |
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| Institution: | (1) Department of Applied Mathematics and Theoretical Physics, University of Cambridge, CB3 9EW Cambridge, UK;(2) Computer Centre, University of Rostov, Rostov-on-Don, USSR;(3) Present address: Pembroke College, Cambridge |
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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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| Keywords: | |
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