Right-Covariant Differential Calculus on Hopf Superalgebra F(Cq2|1)

Çelik S.

Advances in Applied Clifford Algebras, vol.33, no.3, 2023 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 33 Issue: 3
  • Publication Date: 2023
  • Doi Number: 10.1007/s00006-023-01273-z
  • Journal Name: Advances in Applied Clifford Algebras
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, INSPEC, zbMATH
  • Keywords: Differential calculus, Dual Z2-graded Hopf algebra, Right-covariance, Z2-graded Hopf algebra, Z2-graded ⋆-algebra
  • Yıldız Technical University Affiliated: Yes

Abstract

We define a new Z2 -graded quantum (2+1)-space and show that the extended Z2 -graded algebra of polynomials on this Z2 -graded quantum space, denoted by F(Cq2|1) , is a Z2 -graded Hopf algebra. We construct a right-covariant differential calculus on F(Cq2|1) and define a Z2 -graded quantum Weyl algebra and mention a few algebraic properties of this algebra. Finally, we explicitly construct the dual Z2 -graded Hopf algebra of F(Cq2|1) .