A differential calculus on Z$_3$-graded quantum superspace ${\mathbb R}_q(2|1)$
Abstract
We introduce a Z$_3$-graded quantum $(2+1)$-superspace and define Z$_3$-graded Hopf algebra structure on algebra of functions on the Z$_3$-graded quantum superspace. We construct a differential calculus on the Z$_3$-graded quantum superspace, and obtain the corresponding Z$_3$-graded Lie superalgebra. We also find a new Z$_3$-graded quantum supergroup which is a symmetry group of this calculus.
- Publication:
-
arXiv e-prints
- Pub Date:
- September 2015
- DOI:
- 10.48550/arXiv.1509.01492
- arXiv:
- arXiv:1509.01492
- Bibcode:
- 2015arXiv150901492C
- Keywords:
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- Mathematics - Quantum Algebra;
- 17B37;
- 81R60
- E-Print:
- 24 pges, no figures