A New Z<sub>3</sub>-Graded Quantum Space And Its Geometry

Çelik S., Peker A., Bulut F., Temli İ.

INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS, vol.64, no.5, 2025 (SCI-Expanded, Scopus) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 64 Issue: 5
  • Publication Date: 2025
  • Doi Number: 10.1007/s10773-025-05947-1
  • Journal Name: INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, INSPEC, MathSciNet, zbMATH
  • Keywords: Z3-graded algebra, Z3-graded differential calculus, Z3-graded Hopf algebra, Z3-graded q-oscillators, Z3-graded quantum group, Z3-graded space
  • Yıldız Technical University Affiliated: Yes

Abstract

In this article, we initially define an R-matrix with rank 9. Through the application of the "quantum group relation", we derive a Z(3)-graded quantum group, denoted by GL(q)(1|1|1), representing the group of 3x3 matrices. By introducing a Z(3)-graded quantum space, denoted by C-1|1|1 (q) , along with its exterior algebra, we formulate two Z(3)-graded differential calculi which are covariant with respect to the Z(3)-graded Hopf algebra of functions on the Z3-graded quantum group GL(q)(1|1|1).