A New Z3-Graded Quantum Space And Its Geometry

Sultan A. Çelik; Ayse Peker-Dobie; Fatma Bulut; İlknur Temli

doi:10.1007/s10773-025-05947-1

A New Z3-Graded Quantum Space And Its Geometry

Sultan A. Çelik, Ayse Peker-Dobie^*, Fatma Bulut, İlknur Temli

^*Corresponding author for this work

Department of Mathematics Engineering

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

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).

Original language	English
Article number	116
Journal	International Journal of Theoretical Physics
Volume	64
Issue number	5
DOIs	https://doi.org/10.1007/s10773-025-05947-1
Publication status	Published - May 2025

Bibliographical note

Publisher Copyright:
© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2025.

Keywords

Z-graded Hopf algebra
Z-graded algebra
Z-graded differential calculus
Z-graded q-oscillators
Z-graded quantum group
Z-graded space

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10.1007/s10773-025-05947-1

Cite this

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KW - Z-graded differential calculus

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A New Z3-Graded Quantum Space And Its Geometry

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Keywords

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