Cohomological Operators and Covariant Quantum Superalgebras

الأصل · EN

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 GLqp (1|1). In particular, we show that a unique superalgebra, obeyed by the bilinears of fermionic and bosonic noncommutative q-(super)oscillators of GLqp (1|1), is exactly identical to that obeyed by the de Rham cohomological operators. A set of discrete symmetry transformation for a set of GLqp (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.