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Quantum groups, differential calculi and the eigenvalues of the Laplacian

Authors: J. Kustermans, G. J. Murphy and L. Tuset
Journal: Trans. Amer. Math. Soc. 357 (2005), 4681-4717
MSC (2000): Primary 58B32, 58B34
Published electronically: June 29, 2005
MathSciNet review: 2165384
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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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Additional Information

J. Kustermans
Affiliation: Departement Wiskunde, KU Leuven, Celestijnenlaan 200B, 3000 Leuven, Belgium

G. J. Murphy
Affiliation: Department of Mathematics, National University of Ireland, Cork, Ireland

L. Tuset
Affiliation: Faculty of Engineering, University College, Oslo, Norway

Received by editor(s): January 23, 2001
Published electronically: June 29, 2005
Additional Notes: The first author was supported by the National Science Foundation of Flanders
Article copyright: © Copyright 2005 American Mathematical Society

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