Standard Complex for Quantum Lie Algebras

C. Burdik , A. P. Isaev , O. Ogievetsky (1, 2)

1 CPT - Centre de Physique Théorique - UMR 6207
2 CPT - Centre de Physique Théorique - UMR 7332

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.

Domaines: Algèbres quantiques [math.QA]

C. Burdik, A. P. Isaev, O. Ogievetsky. Standard Complex for Quantum Lie Algebras. 2000. ⟨hal-00473331⟩