2003/09/30 by R. P. Malik, R P Malik
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #hep-th
paper · pdf · doi:10.1088/0305-4470/37/34/013
published as J.Phys. A37 (2004) 8383-8400 · LaTeX file, 21 pages
openalex publication_date 2004/08/12 · arxiv created 2004/08/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
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 quantum 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 transformations for a set of GL qp (1|1) covariant quantum superalgebras turns out to be the analogue of the Hodge duality * operation of differential geometry. A connection with an extended Becchi–Rouet–Stora–Tyutin (BRST) algebra obeyed by the conserved and nilpotent (anti-)BRST and (anti-)co-BRST charges, the conserved ghost charge and a conserved bosonic charge (which is equal to the anticommutator of (anti-)BRST and (anti-)co-BRST charges) is also established.