E. V. Damaskinsky, P. P. Kulish, M. A. Sokolov
Gauss Decompositions for Quantum Groups and Supergroups
Preprint series: ESI preprints

MSC:

16W30 Coalgebras, bialgebras, Hopf algebras, See also {57T05,

17B37 Quantum groups and related deformations, See also {16W30, 81R50, 82B23}

58B30 Noncommutative differential geometry and topology, See also {46L30, 46L87, 46L89}

81R50 Quantum groups and related algebraic methods, See Also {16W30, 17B37}

Abstract: The Gauss decompositions of the quantum groups, related to classical
Lie groups and supergroups are considered by the elementary algebraic and
$R$-matrix methods. The commutation relations between new basis generators
(which are introduced by the decomposition) are described in some details.
It is shown that the reduction of the independent generator number
in the new basis
to the dimension of related classical (super) group is possible. The classical
expression for (super) determinant through the Gauss decomposition
generators is not changed in the deformed case. The symplectic quantum
group $Sp_q(2)$ and supergroups $GL_q(1|1), GL_q(2|1)$ are considered as
examples.

Keywords: quantum group, supergroup, Gauss decomposition