TITLE:
On Some Properties of the Heisenberg Laplacian
AUTHORS:
M. E. Egwe
KEYWORDS:
Heisenberg Group; Heisenberg Laplacian; Factorization; Universal Enveloping Algebra; Solvability
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.2 No.5,
September
26,
2012
ABSTRACT: Let IHn be the (2n+1) -dimensional Heisenberg group and let Lα and be the sublaplacian and central element of the Lie algebra of IHn respectively. Forα=0 denote by L0=L the Heisenberg Laplacian and let K ∈Aut(IHn) be a compact subgroup of Au-tomorphism of IHn. In this paper, we give some properties of the Heisenberg Laplacian and prove that L and T generate the K-invariant universal enveloping algebra, U(hn)k of IHn.