A Two-Parameter Quantum (2+1)-Superspace and its Deformed Derivation Algebra as Hopf Superalgebra

Ozavsar M.

ADVANCES IN APPLIED CLIFFORD ALGEBRAS, vol.23, no.3, pp.741-756, 2013 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 23 Issue: 3
  • Publication Date: 2013
  • Doi Number: 10.1007/s00006-013-0394-4
  • Journal Name: ADVANCES IN APPLIED CLIFFORD ALGEBRAS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.741-756
  • Keywords: Quantum superspace, Hopf superalgebra, Derivation algebra, Noncommutative differential calculus, COMPACT MATRIX PSEUDOGROUPS, DIFFERENTIAL-CALCULUS, NONCOMMUTATIVE GEOMETRY, SUPERSPACE, PLANE, DEFORMATION, CONNECTIONS, DUALITY, SPACE
  • Yıldız Technical University Affiliated: Yes

Abstract

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.