A Two-Parameter Quantum (2+1)-Superspace and its Deformed Derivation Algebra as Hopf Superalgebra - Ozavsar, Muttalip (SPRINGER BASEL AG, 2013)
As is well known, a Hopf algebra setting is an efficient tool to study some geometric structures such as the Maurer-Cartan invariant forms and the corresponding vector fields on a noncommutative space. In this study we introduce a two-parameter quantum (2+1)-superspace with a Hopf superalgebra structure.We also define some derivation operators acting on this quantum superspace, and we show that the algebra of these derivations is a Hopf superalgebra. Furthermore it will be shown how the derivation operators lead to a bicovariant differential calculus on the two- parameter quantum (2+1)-superspace. In conclusion, based on the bicovariant differential calculus, the Maurer-Cartan right invariant differential forms and the corresponding quantum Lie superalgebra are given.
Keywords: Quantum superspace; Hopf superalgebra; Derivation algebra; Noncommutative differential calculus; COMPACT MATRIX PSEUDOGROUPS; DIFFERENTIAL-CALCULUS; NONCOMMUTATIVE GEOMETRY; SUPERSPACE; PLANE; DEFORMATION; CONNECTIONS; DUALITY; SPACE; Mathematics; Physics