q-Epsilon tensor for quantum and braided spaces

Abstract

The machinery of braided geometry introduced previously is used now to construct the $\epsilon$ `totally antisymmetric tensor' on a general braided vector space determined by R-matrices. This includes natural $q$-Euclidean and $q$-Minkowski spaces. The formalism is completely covariant under the corresponding quantum group such as $\widetilde{S{O}_q(4)}$ or $\widetilde{S{O}_q(1,3)}$. The Hodge $\ast$ operator and differentials are also constructed in this approach.

24 pages, substantative revision - decided to include material on Hodge * operator previously omitted. Added a figure

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Cited by in corpus (14)

• Quantum Groups and Noncommutative Geometry
• Introduction to Braided Geometry and $q$-Minkowski Space
• *-Structures on Braided Spaces
• Quantum group covariant (anti)symmetrizers, epsilon-tensors, vielbein, Hodge map and Laplacian
• Noncommutative cohomology and electromagnetism on $C_q[S{L}_2]$ at roots of unity
• Calculi, Hodge operators and Laplacians on a quantum Hopf fibration
• Meaning of Noncommutative Geometry and the Planck-Scale Quantum Group
• Duality Principle and Braided Geometry
• Some remarks on the {$q$}-Poincare algebra in R-matrix form
• On the hermiticity of q-differential operators and forms on the quantum Euclidean spaces R_q^N
• Quantum determinants
• Spinor calculus for q-deformed quantum spaces II
• Quasi-{$\ast$} Structure on {$q$}-Poincare algebras
• Conservation laws for a $q$-deformed nonrelativistic particle