Defining Relations for Lie Superalgebras with Cartan Matrix |
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Authors: | Pavel Grozmann Dimitry Leites |
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Affiliation: | (1) Department of Mathematics, University of Stockholm, Roslagsv. 101, Kräftriket hus 6, S-106 91 Stockholm, Sweden |
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Abstract: | We completely describe presentations of Lie superalgebras with Cartan matrix if they are simple -graded of polynomial growth. Such matrices can be neither integer nor symmetrizable. There are non-Serre relations encountered. In certain cases there are infinitely many relations. For symmetrizable Cartan matrices similar (but not identical) presentations are obtained by Yamane who also considered q-quantized versions of these relations (q-alg 9603015). Yamane did not try to find out which of the relations he offers constitute a minimal set generating all other relations; contrariwise we give minimal sets of defining relations and in various cases our relations look much simpler than Yamane's (though still very complicated in some cases). |
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Keywords: | Lie superalgebras cohomology presentations defining relations |
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