A New Z3-Graded Quantum Space And Its Geometry - Celik, Sultan A.; Peker-Dobie, Ayse; Bulut, Fatma; Temli, Ilknur (SPRINGER/PLENUM PUBLISHERS, 2025)
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).
Keywords: Z(3)-graded space; Z(3)-graded algebra; Z(3)-graded quantum group; Z(3)-graded Hopf algebra; Z(3)-graded differential calculus; Z(3)-graded q-oscillators; DIFFERENTIAL-CALCULUS; DEFORMATION; Physics