A procedure to obtain bicovariant differential calculi on matrix quantum groups is presented. The construction is based on the description of the matrix quantum group as a quantized universal enveloping algebra by the use of exponential coordinates. The procedure is illustrated by applying it to the two-dimensional solvable quantum group and the Heisenberg quantum group.

Universal enveloping algebras of Lie algebras (msc 16S30), Rings and algebras with additional structure (msc 16Wxx), Universal enveloping (super)algebras (msc 17B35), Quantum groups (quantized enveloping algebras) and related deformations (msc 17B37), Quantum groups and related algebraic methods (msc 81R50)
CWI
Department of Analysis, Algebra and Geometry [AM]

van den Hijligenberg, N.W, & Martini, R. (1995). From exponential coordinates to bicovariant differential calculi on matrix quantum groups. Department of Analysis, Algebra and Geometry [AM]. CWI.