Cartan calculus on the superalgebra (Formula present)


Çelik S.

Mathematical Communications, vol.28, no.2, pp.213-234, 2023 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 28 Issue: 2
  • Publication Date: 2023
  • Journal Name: Mathematical Communications
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, zbMATH, Directory of Open Access Journals
  • Page Numbers: pp.213-234
  • Keywords: Cartan calculus, Clifford superalgebra, differential calculus, Hopf superalgebra, inner derivation, Lie derivative, Quantum superspaces
  • Yıldız Technical University Affiliated: Yes

Abstract

By analogy with the classical case, noncommutative differential calculus on a quantum superspace can be extended to the Cartan calculus by introducing inner derivations and Lie derivatives. So, to give the Cartan calculus on the algebra of functions on quantum (2+1)-superspace (Formula present) we first introduce two left-covariant differential calculi over (Formula present) and extend one of these calculi by adding inner derivations and Lie derivatives to the calculus. We also introduce tensor product realization of the wedge product of forms.