Deformation of the Heisenberg Algebra inside $gl(3,\mathbb{K})$

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dc.creatorFregier, Yael
dc.date2004-03-24
dc.date.accessioned2026-07-07T05:06:42Z
dc.date.available2026-07-07T05:06:42Z
dc.descriptionWe study non-trivial deformations of the natural imbedding of the Lie algebra $\fh_1$ of lower triangular matrices (the Heisenberg Lie algebra) into $gl(3,\mathbb{K})$, where $\mathbb{K}=\mathbb{R}$ or $|mathbb{C}$. Our first result is the calculation of the first cohomology space $H^1(\fh_1;gl(3,\mathbb{K}))$. We prove that there are no obstructions for integrability of infinitesemal deformation and, furthermore, give an explicit formula for the most general deformation.
dc.description15 pages
dc.identifierhttps://arxiv.org/abs/math/0403410
dc.identifierhttp://arxiv.org/abs/math/0403410
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/70574
dc.subjectRepresentation Theory
dc.subject17B99
dc.titleDeformation of the Heisenberg Algebra inside $gl(3,\mathbb{K})$
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