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Journal of Mathematical Physics 49 (2008) 073512

BRST Operator for Quantum Lie Algebras: Relation to Bar Complex

V. G. Gorbounov, A. P. Isaev, O. V. Ogievetsky 1

(2008)

Quantum Lie algebras (an important class of quadratic algebras arising in the Woronowicz calculus on quantum groups) are generalizations of Lie (super) algebras. Many notions from the theory of Lie (super)algebras admit ``quantum'' generalizations. In particular, there is a BRST operator Q (Q^2=0) which generates the differential in the Woronowicz theory and gives information about (co)homologies of quantum Lie algebras. In our previous papers a recurrence relation for the operator Q for quantum Lie algebras was given and solved. Here we consider the bar complex for q-Lie algebras and its subcomplex of q-antisymmetric chains. We establish a chain map (which is an isomorphism) of the standard complex for a q-Lie algebra to the subcomplex of the antisymmetric chains. The construction requires a set of nontrivial identities in the group algebra of the braid group. We discuss also a generalization of the standard complex to the case when a q-Lie algebra is equipped with a grading operator.

1 :	Centre de Physique Théorique (CPT)
	CNRS : FR2291 – Université de Provence - Aix-Marseille I – Université de la Méditerranée - Aix-Marseille II – Université Sud Toulon Var

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:

Mathématiques/Algèbres quantiques Mathématiques/Physique mathématique Physique/Physique mathématique

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Contributeur : Elizabeth Bernardo <>

Soumis le : Mercredi 9 Janvier 2008, 09:42:45

Dernière modification le : Mardi 6 Janvier 2009, 15:19:17