Differential calculi on the Z3-graded Hopf algebra F(C~q1|1|1)

ÇELİK S.

Arabian Journal of Mathematics, vol.14, no.2, pp.197-218, 2025 (ESCI, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 14 Issue: 2
  • Publication Date: 2025
  • Doi Number: 10.1007/s40065-025-00517-z
  • Journal Name: Arabian Journal of Mathematics
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
  • Page Numbers: pp.197-218
  • Yıldız Technical University Affiliated: Yes

Abstract

Considering a Z3-graded 3-dimensional space, we develop Z3-graded differential calculi on the algebra of functions defined on this space, which is a Z3-graded Hopf algebra. We demonstrate that these differential calculi admit a ∗-operation. Additionally, we discover a new Z3-graded upper triangular quantum group and explicitly define its Z3-graded Hopf algebraic structure. We also show in detail that this quantum group is the symmetry group of one of these calculi.