Dimitry Leites

On the defining relations of quantum superalgebras

In defining quantum superalgebras, extra relations need to be added to the Serre-like relations. They are obtained for slq(m, n) and ospq(m, 2n) usingq-oscillator representations.

Defining Relations for Lie Superalgebras with Cartan Matrix

We completely describe presentations of Lie superalgebras with Cartan matrix if they are simple ℤ-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 Yamanes (though still very complicated in some cases).

HOW TO QUANTIZE THE ANTIBRACKET

AbstractWe show that in contrast to

Structures of G(2) Type and Nonintegrable Distributions in Characteristic p

{\mathfrak{p}}o(2n|m)

Lie superalgebras of supermatrices of complex size. Their generalizations and related integrable systems

, its quotient modulo center, the Lie superalgebra

Orthogonal polynomials of a discrete variable and Lie algebras of complex-size matrices

{\mathfrak{h}}(2n|m)