Standard Complex for Quantum Lie Algebras

Abstract

For a quantum Lie algebra $\Gamma$, let ${\Gamma }^{\wedge }$ be its exterior extension (the algebra ${\Gamma }^{\wedge }$ is canonically defined). We introduce a differential on the exterior extension algebra ${\Gamma }^{\wedge }$ which provides the structure of a complex on ${\Gamma }^{\wedge }$. In the situation when $\Gamma$ is a usual Lie algebra this complex coincides with the "standard complex". The differential is realized as a commutator with a (BRST) operator $Q$ in a larger algebra ${\Gamma }^{\wedge }[\Omega ]$, with extra generators canonically conjugated to the exterior generators of ${\Gamma }^{\wedge }$. A recurrent relation which defines uniquely the operator $Q$ is given.

10 pages, LaTeX. Report given at XXIII Int. Colloquium on Group Theoretical Methods in Physics, July 31 - August 05, 2000, Dubna (Russia)

References in corpus (1)

• On the algebraic structure of differential calculus on quantum groups

Cited by in corpus (2)

• BRST operators for W algebras
• BRST charges for finite nonlinear algebras