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http://dx.doi.org/10.4134/CKMS.2013.28.3.501

LAPLACIAN ON A QUANTUM HEISENBERG MANIFOLD  

Lee, Hyun Ho (Department of Mathematics University of Ulsan)
Publication Information
Communications of the Korean Mathematical Society / v.28, no.3, 2013 , pp. 501-509 More about this Journal
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 $C^*$-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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