BRST Operator for Quantum Lie Algebras and Differential Calculus on Quantum Groups
Teoretičeskaâ i matematičeskaâ fizika, Tome 129 (2001) no. 2, pp. 298-316
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For a Hopf algebra $\mathcal A$, we define the structures of differential complexes on two dual exterior Hopf algebras: (1) an exterior extension of $\mathcal A$ and (2) an exterior extension of the dual algebra $\mathcal A^*$. The Heisenberg double of these two exterior Hopf algebras defines the differential algebra for the Cartan differential calculus on $\mathcal A$. The first differential complex is an analogue of the de Rham complex. When $\mathcal A^*$ is a universal enveloping algebra of a Lie (super)algebra, the second complex coincides with the standard complex. The differential is realized as an (anti)commutator with a BRST operator $Q$. We give a recursive relation that uniquely defines the operator $Q$. We construct the BRST and anti-BRST operators explicitly and formulate the Hodge decomposition theorem for the case of the quantum Lie algebra $U_{\mathrm q}(gl(N))$.
@article{TMF_2001_129_2_a9,
author = {A. P. Isaev and O. V. Ogievetskii},
title = {BRST {Operator} for {Quantum} {Lie} {Algebras} and {Differential} {Calculus} on {Quantum} {Groups}},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {298--316},
publisher = {mathdoc},
volume = {129},
number = {2},
year = {2001},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2001_129_2_a9/}
}
TY - JOUR AU - A. P. Isaev AU - O. V. Ogievetskii TI - BRST Operator for Quantum Lie Algebras and Differential Calculus on Quantum Groups JO - Teoretičeskaâ i matematičeskaâ fizika PY - 2001 SP - 298 EP - 316 VL - 129 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_2001_129_2_a9/ LA - ru ID - TMF_2001_129_2_a9 ER -
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A. P. Isaev; O. V. Ogievetskii. BRST Operator for Quantum Lie Algebras and Differential Calculus on Quantum Groups. Teoretičeskaâ i matematičeskaâ fizika, Tome 129 (2001) no. 2, pp. 298-316. http://geodesic.mathdoc.fr/item/TMF_2001_129_2_a9/