Contragredient Lie Superalgebras Research Articles

UniversalR-matrix for quantized (super)algebras

For quantum deformations of finite-dimensional contragredient Lie (super)algebras we give an explicit formula for the universalR-matrix. This formula generalizes the analogous formulae for quantized semisimple Lie algebras obtained by M. Rosso, A. N. Kirillov, and N. Reshetikhin, Ya. S. Soibelman, and S. Z. Levendorskii. Our approach is based on careful analysis of quantized rank 1 and 2 (super)algebras, a combinatorial structure of the root systems and algebraic properties ofq-exponential functions. We don't use quantum Weyl group.

AUTOMORPHISMS OF SIMPLE LIE SUPERALGEBRAS

This paper gives an enumeration of the outer automorphisms of simple finite-dimensional complex Lie superalgebras, the nonisomorphic infinite-dimensional Lie superalgebras associated with these automorphisms, and the systems of simple roots in contragredient Lie superalgebras (finite-dimensional and associated with a finite-dimensional simple Lie superalgebra and automorphisms of this Lie superalgebra). Bibliography: 6 titles.