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Standard Complex for Quantum Lie Algebras

Authors :
C. Burdik
O. V. Ogievetsky
A. P. Isaev
Centre de Physique Théorique - UMR 6207 (CPT)
Université de la Méditerranée - Aix-Marseille 2-Université de Provence - Aix-Marseille 1-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS)
Centre de Physique Théorique - UMR 7332 (CPT)
Aix Marseille Université (AMU)-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS)
Centre National de la Recherche Scientifique (CNRS)-Université de Toulon (UTLN)-Université de Provence - Aix-Marseille 1-Université de la Méditerranée - Aix-Marseille 2
Ogievetsky, Oleg
Publication Year :
2000
Publisher :
HAL CCSD, 2000.

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

Details

Language :
English
Database :
OpenAIRE
Accession number :
edsair.doi.dedup.....8702d62fce9c652120683f9e803b908b