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

^*Bu çalışma için yazışmadan sorumlu yazar

Matematik Bölümü

Araştırma sonucu: Dergiye katkı › Makale › bilirkişi

1 Atıf (Scopus)

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).

Orijinal dil	İngilizce
Makale numarası	116
Dergi	International Journal of Theoretical Physics
Hacim	64
Basın numarası	5
DOI'lar	https://doi.org/10.1007/s10773-025-05947-1
Yayın durumu	Yayınlandı - May 2025

Bibliyografik not

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

Belgeye Erişim

10.1007/s10773-025-05947-1

Diğer Dosyalar ve Linkler

Link to publication in Scopus

Alıntı Yap

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title = "A New Z3-Graded Quantum Space And Its Geometry",

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\textasciitilde{}q(1|1|1), representing the group of 3×3 matrices. By introducing a Z3-graded quantum space, denoted by C\textasciitilde{}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\textasciitilde{}q(1|1|1).",

keywords = "Z-graded Hopf algebra, Z-graded algebra, Z-graded differential calculus, Z-graded q-oscillators, Z-graded quantum group, Z-graded space",

author = "\{A. {\c C}elik\}, Sultan and Ayse Peker-Dobie and Fatma Bulut and İlknur Temli",

note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2025.",

year = "2025",

month = may,

doi = "10.1007/s10773-025-05947-1",

language = "English",

volume = "64",

journal = "International Journal of Theoretical Physics",

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AU - A. Çelik, Sultan

AU - Peker-Dobie, Ayse

AU - Bulut, Fatma

AU - Temli, İlknur

N1 - Publisher Copyright: © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2025.

PY - 2025/5

Y1 - 2025/5

N2 - 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).

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KW - Z-graded Hopf algebra

KW - Z-graded algebra

KW - Z-graded differential calculus

KW - Z-graded q-oscillators

KW - Z-graded quantum group

KW - Z-graded space

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DO - 10.1007/s10773-025-05947-1

M3 - Article

AN - SCOPUS:105003479192

SN - 0020-7748

VL - 64

JO - International Journal of Theoretical Physics

JF - International Journal of Theoretical Physics

IS - 5

M1 - 116

ER -

A New Z3-Graded Quantum Space And Its Geometry

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