Standard complex for quantum Lie algebras |
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| Authors: | C Burdik A P Isaev O V Ogievetsky |
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| Institution: | (1) Department of Mathematics, Faculty of Nuclear Sciences and Physical Engineering, Prague, Czech Republic;(2) Center of Theoretical Physics, Luminy, Marseille, France;(3) Theoretical Department, Lebedev Institute of Physics, Moscow, Russia;(4) Bogolyubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna, Moscow oblast, 141980, Russia |
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| Abstract: | For a quantum Lie algebra Γ, let Γ^ be its exterior extension (the algebra Γ^ is canonically defined). We introduce a differential on the exterior extension algebra Γ^ which provides the structure of a complex on Γ^. In the situation when Γ 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 Γ^Ω], with extra generators canonically conjugated to the exterior generators of Γ^. A recurrent relation which uniquely defines the operator Q is given. |
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