Shahn Majid
q-Epsilon Tensor for Quantum and Braided Spaces
The paper is published: J. Math. Phys. 36, 4 (1995) 1991-2007

MSC:

17B37 Quantum groups and related deformations, See also {16W30, 81R50, 82B23}

58B30 Noncommutative differential geometry and topology, See also {46L30, 46L87, 46L89}

58A14 Hodge theory, See also {14C30, 14Fxx, 32J25, 32S35}

81R50 Quantum groups and related algebraic methods, See Also {16W30, 17B37}

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 $\widetilde{SO_q(4)}$ or
$\widetilde{SO_q(1,3)}$. The Hodge $*$ operator and differentials are also
constructed in this approach.

Keywords: quantum group covariance, braid statistics, totally antisymmetric tensor, quantum spaces of R-matrix type, q-Euclidean spaces, braided geometry, braided vector space, q-Minkowski spaces, Hodge *-operator