Differential geometry of the quantum supergroup GLH,H′ (1|1)

ÇELİK S., Temli I.

Reports on Mathematical Physics, vol.93, no.3, pp.371-391, 2024 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 93 Issue: 3
  • Publication Date: 2024
  • Doi Number: 10.1016/s0034-4877(24)00044-2
  • Journal Name: Reports on Mathematical Physics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, INSPEC, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.371-391
  • Keywords: bi-covariant differential calculus, h-deformed Lie superalgebra, h-deformed superplanes, super inner derivations, super Lie derivatives
  • Yıldız Technical University Affiliated: Yes

Abstract

In this paper, we construct a bi-covariant (h,h′)-deformed differential calculus on the Hopf superalgebra of functions on the quantum supergroup GLh.h′ (1|1) and obtain an extended differential calculus (Cartan calculus) by including inner derivations and Lie derivatives. In doing so, we use left-Cartan-Maurer 1-forms and left-vector fields.