# LAPLACIAN ON A QUANTUM HEISENBERG MANIFOLD

Lee, Hyun Ho

• Published : 2013.07.31
• 21 9

#### 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

#### References

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#### Cited by

1. A note on nonlinear σ-models in noncommutative geometry vol.19, pp.01, 2016, https://doi.org/10.1142/S0219025716500065

#### Acknowledgement

Supported by : University of Ulsan