Hodge and Laplace-Beltrami Operators for Bicovariant Differential Calculi on Quantum Groups

Details Hodge and Laplace-Beltrami Operators for Bicovariant Differential Calculi on Quantum Groups Hodge and Laplace-Beltrami Operators for Bicovariant Differential Calculi on Quantum Groups

1999-02-23

arxiv.org/abs/math/9902130v1

Mathematics

Quantum Algebra

30 pages, LaTeX2e

Scientific paper

For bicovariant differential calculi on quantum matrix groups a generalisation of classical notions such as metric tensor, Hodge operator, codifferential and Laplace-Beltrami operator for arbitrary k-forms is given. Under some technical assumptions it is proved that Woronowicz' external algebra of left-invariant differential forms either contains a unique form of maximal degree or it is infinite dimensional. Using Jucys-Murphy elements of the Hecke algebra the eigenvalues of the Laplace-Beltrami operator for the Hopf algebra O(SLq(N)) are computed.

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