Cohomological Operators and Covariant Quantum Superalgebras

Details Cohomological Operators and Covariant Quantum Superalgebras Cohomological Operators and Covariant Quantum Superalgebras

2003-09-12

arxiv.org/abs/hep-th/0309127v5

J.Phys. A37 (2004) 8383-8400

Physics

High Energy Physics

High Energy Physics - Theory

LaTeX file, 21 pages

Scientific paper

10.1088/0305-4470/37/34/013

We obtain an interesting realization of the de Rham cohomological operators of differential geometry in terms of the noncommutative q-superoscillators for the supersymmetric quantum group GL_{qp} (1|1). In particular, we show that a unique superalgebra, obeyed by the bilinears of fermionic and bosonic noncommutative q-(super)oscillators of GL_{qp} (1|1), is exactly identical to that obeyed by the de Rham cohomological operators. A set of discrete symmetry transformation for a set of GL_{qp} (1|1) covariant superalgebras turns out to be the analogue of the Hodge duality * operation of differential geometry. A connection with an extended BRST algebra obeyed by the nilpotent (anti-)BRST and (anti-)co-BRST charges, the ghost charge and a bosonic charge (which is equal to the anticommutator of (anti-)BRST and (anti-)co-BRST charges) is also established.

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