Laplacian on a quantum Heisenberg manifold
Commun. Korean Math. Soc. 2013 Vol. 28, No. 3, 501-509
https://doi.org/10.4134/CKMS.2013.28.3.501
Printed July 1, 2013
Hyun Ho Lee
University of Ulsan
Abstract : In this paper we give a definition of the Hodge type Laplacian $\Delta$ on a non-commutative manifold which is the smooth dense subalgebra of a $C\sp*$-algebra. We prove that the Laplacian on a quantum Heisenberg manifold is an elliptic operator in the sense that $(\Delta+1)^{-1}$ is compact.
Keywords : quantum Heisenberg manifolds, Laplacian, elliptic operator
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