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The BRST operator of quantum symmetries: the quantum analogs of Donaldson invariants. (English) Zbl 0910.53049
The authors consider a gauge theory in which the role of gauge group is played by a noncommutative Hopf algebra and the base space is given by a noncommutative algebra. They construct a BRST operator for this situation and show that the nilpotency of the BRST operator can either be derived from the Hopf axioms of the quantum group symmetries or from the Jacobi identity of their quantum Lie algebra. They extend the BRST operator to topological transformations and derive the quantum analogs of the descent equations for the Donaldson invariant polynomials from the construction of invariant polynomials of the curvature.

MSC:
53Z05 Applications of differential geometry to physics
81R50 Quantum groups and related algebraic methods applied to problems in quantum theory
81T13 Yang-Mills and other gauge theories in quantum field theory
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