A NEW QUANTUM SUPERGROUP AND ITS GAUSS DECOMPOSITION

Abstract

We get a new quantum supergroup (Hopf superalgebra), denoted by GL(q) (211), by using the standard method (the RU-relation) with an R-matrix which is a solution of the quantum Yang- Baxter equation. We give the Gauss decomposition of a matrix in GL(q) (211) and considering the three matrices in the decomposition in pairs, we show that two superalgebras formed by matrix elements of these matrices are Hopf superalgebras.