Abstract
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 \(\mathcal{O}\)(SL q (N)) are computed.
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Heckenberger, I. Hodge and Laplace–Beltrami Operators for Bicovariant Differential Calculi on Quantum Groups. Compositio Mathematica 123, 329–354 (2000). https://doi.org/10.1023/A:1002043604471
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DOI: https://doi.org/10.1023/A:1002043604471