On the quantum group SLq(2)

Joseph Bernstein, Tanya Khovanova

Research output: Contribution to journalArticlepeer-review


We start with the observation that the quantum group SLq(2), described in terms of the algebra of functions has a quantum subgroup, which is just a usual Cartan group. Based on this observation, we develop a general method of constructing quantum groups with similar property. We also develop this method in the language of quantized universal enveloping algebras, which is another common method of studying quantum groups. We carry out our method in detail for root systems of type SL(2); as a byproduct, we find a new series of quantum groups-metaplectic groups of SL(2)-type. Representations of these groups can provide interesting examples of bimodule categories over monoidal category of representations of SLq(2).

Original languageEnglish
Pages (from-to)691-708
Number of pages18
JournalCommunications in Mathematical Physics
Issue number3
StatePublished - 1996


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