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On Some Properties of the Heisenberg Laplacian
Department of Mathematics, Universty of Ibadan
- 1 Department of Mathematics, Universty of Ibadan
Advances in Pure Mathematics·Volume 02 (2012)·Pages 354–357·Published 25 September 2012·DOI10.4236/apm.2012.25051
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Abstract
Let IH n be the (2n+1) -dimensional Heisenberg group and let L α and be the sublaplacian and central element of the Lie algebra of IH n respectively. Forα=0 denote by L 0 =L the Heisenberg Laplacian and let K ∈Aut(IH n ) be a compact subgroup of Au-tomorphism of IH n . 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(h n ) k of IH n .
KeywordsHeisenberg GroupHeisenberg LaplacianFactorizationUniversal Enveloping AlgebraSolvability
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