BRST Operator for Quantum Lie Algebras: Relation to Bar Complex

Simple item page
dc.creatorGorbounov, V. G.
dc.creatorIsaev, A. P.
dc.creatorOgievetsky, O. V.
dc.date2007-11-27
dc.date.accessioned2026-07-07T08:45:17Z
dc.date.available2026-07-07T08:45:17Z
dc.descriptionQuantum 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.
dc.description20 pages
dc.identifierhttps://arxiv.org/abs/0711.4133
dc.identifierhttp://arxiv.org/abs/0711.4133
dc.identifierTheor. Math. Phys. 139 No. 1 (2004) 473
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/142921
dc.subjectQuantum Algebra
dc.subjectMathematical Physics
dc.subject81R50
dc.titleBRST Operator for Quantum Lie Algebras: Relation to Bar Complex
dc.typetext

Files

Collections

arXiv