On Poisson-Lie structure on the external algebra of the classical Lie groups

Abstract

The general expression for the bicovariant bracket for odd generators of the external algebra on a Poisson-Lie group is given. It is shown that the graded Poisson-Lie structures derived before for $GL(N)$ and $SL(N)$ are the special cases of this bracket. The formula is the universal one and can be applied to the case of any matrix Lie group.

12 pages

References in corpus (6)

• Differential Geometry on Linear Quantum Groups
• GLq(N)-Covariant Quantum Algebras and Covariant Differential Calculus
• Differential Calculus on Quantum Spaces and Quantum Groups
• Poincare'-Birkhoff-Witt property for bicovariant differential algebras on simple quantum groups
• Differential Calculi on Quantum (Sub-) Groups and Their Classical Limit
• The Differential Calculus on Quantum Linear Groups