Faithful representations of minimal dimension of current Heisenberg Lie algebras

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dc.creatorCagliero, L.
dc.creatorRojas, N.
dc.date2008-03-07
dc.date.accessioned2026-07-07T09:25:39Z
dc.date.available2026-07-07T09:25:39Z
dc.descriptionGiven a Lie algebra $\mathfrak{g}$ over a field of characteristic zero $k$, let $μ(\mathfrak{g})=\min\{\dim π: π\text{is a faithful representation of}\mathfrak{g}\}$. Let $\mathfrak{h}_{m}$ be the Heisenberg Lie algebra of dimension $2m+1$ over $k$ and let $k[t]$ be the polynomial algebra in one variable. Given $m\in\mathbb{N}$ and $p\in k[t]$, let $\mathfrak{h}_{m,p}=\mathfrak{h}_m\otimes k[t]/(p)$ be the current Lie algebra associated to $\mathfrak{h}_m$ and $k[t]/(p)$, where $(p)$ is the principal ideal in $k[t]$ generated by $p$. In this paper we prove that $ mu(\mathfrak{h}_{m,p}) = m °p + \left \lceil 2\sqrt{°p} \right\rceil$.
dc.description14 pages
dc.identifierhttps://arxiv.org/abs/0803.1076
dc.identifierhttp://arxiv.org/abs/0803.1076
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/156474
dc.subjectRepresentation Theory
dc.subjectMathematical Physics
dc.subject17B10, 17B30
dc.titleFaithful representations of minimal dimension of current Heisenberg Lie algebras
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