Quantum groups, differential calculi and the eigenvalues of the Laplacian

Kustermans, J.; Murphy, G.; Tuset, L.

doi:10.1090/S0002-9947-05-03971-1

Quantum groups, differential calculi and the eigenvalues of the Laplacian
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by J. Kustermans, G. J. Murphy and L. Tuset PDF

Trans. Amer. Math. Soc. 357 (2005), 4681-4717 Request permission

Abstract:

We study $*$-differential calculi over compact quantum groups in the sense of S.L. Woronowicz. Our principal results are the construction of a Hodge operator commuting with the Laplacian, the derivation of a corresponding Hodge decomposition of the calculus of forms, and, for Woronowicz’ first calculus, the calculation of the eigenvalues of the Laplacian.

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