Z3-graded differential geometry of the quantum plane
- 18 July 2002
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 35 (30), 6307-6318
- https://doi.org/10.1088/0305-4470/35/30/308
Abstract
In this work, the Z$_3$-graded differential geometry of the quantum plane is constructed. The corresponding quantum Lie algebra and its Hopf algebra structure are obtained. The dual algebra, i.e. universal enveloping algebra of the quantum plane is explicitly constructed and an isomorphism between the quantum Lie algebra and the dual algebra is given.Keywords
This publication has 13 references indexed in Scilit:
- Cubic root of Klein-Gordon equationPhysics Letters B, 2000
- International Journal of Modern Physics A, 2000
- A calculus based on a q-deformed Heisenberg algebraThe European Physical Journal C, 1999
- Universal ZN-graded differential calculusJournal of Geometry and Physics, 1997
- The cubic chessboardClassical and Quantum Gravity, 1997
- Z 3-Graded exterior differential calculus and gauge theories of higher orderLetters in Mathematical Physics, 1996
- Remarks on bicovariant differential calculi and exterior Hopf algebrasLetters in Mathematical Physics, 1993
- A class of bicovariant differential calculi on hopf algebrasLetters in Mathematical Physics, 1992
- Z 3 -graded algebras and the cubic root of the supersymmetry translationsJournal of Mathematical Physics, 1992
- Covariant differential calculus on the quantum hyperplaneNuclear Physics B - Proceedings Supplements, 1991