Cohomological Operators and Covariant Quantum Superalgebras

TL;DR

This paper establishes a novel connection between de Rham cohomological operators and noncommutative q-superoscillators within supersymmetric quantum groups, revealing a superalgebra structure and symmetries analogous to differential geometry concepts.

Contribution

It introduces a unique superalgebra realized through noncommutative q-superoscillators that mirrors de Rham cohomological operators and explores its symmetry properties and relation to BRST algebra.

Findings

Superalgebra identical to de Rham cohomological operators

Discrete symmetry transformation analogous to Hodge duality

Connection established with extended BRST algebra

Abstract

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.