A New Z3-Graded Quantum Space And Its Geometry

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

International Journal of Theoretical Physics, cilt.64, sa.5, 2025 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 64 Sayı: 5
  • Basım Tarihi: 2025
  • Doi Numarası: 10.1007/s10773-025-05947-1
  • Dergi Adı: International Journal of Theoretical Physics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: Z3-graded algebra, Z3-graded differential calculus, Z3-graded Hopf algebra, Z3-graded q-oscillators, Z3-graded quantum group, Z3-graded space
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

In this article, we initially define an R-matrix with rank 9. Through the application of the "quantum group relation", we derive a Z3-graded quantum group, denoted by GL~q(1|1|1), representing the group of 3×3 matrices. By introducing a Z3-graded quantum space, denoted by C~q1|1|1, along with its exterior algebra, we formulate two Z3-graded differential calculi which are covariant with respect to the Z3-graded Hopf algebra of functions on the Z3-graded quantum group GL~q(1|1|1).