Hodge and Laplace-Beltrami Operators for Bicovariant Differential Calculi on Quantum Groups
نویسنده
چکیده
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.
منابع مشابه
De Rham Cohomology and Hodge Decomposition for Quantum Groups
ISTVÁN HECKENBERGER and AXEL SCHÜLER Abstra t Let Γ = Γτ,z be one of the N -dimensional bicovariant first order differential calculi for the quantum groups GLq(N), SLq(N), SOq(N), or Spq(N), where q is a transcendental complex number and z is a regular parameter. It is shown that the de Rham cohomology of Woronowicz’ external algebra Γ coincides with the de Rham cohomologies of its left-coinvar...
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