Irreducibility criterion for the set of two matrices

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dc.creatorKosyak, Alexandre
dc.date2008-07-29
dc.date2008-11-02
dc.date.accessioned2026-07-07T10:14:20Z
dc.date.available2026-07-07T10:14:20Z
dc.descriptionWe give the criterion for the irreducibility, the Schur irreducibility and the indecomposability of the set of two $n\times n$ matrices $Λ_n$ and $A_n$ in terms of the subalgebra associated with the "support" of the matrix $A_n$, where $Λ_n$ is a diagonal matrix with different non zeros eigenvalues and $A_n$ is an arbitrary one. The list of all maximal subalgebras of the algebra ${\rm Mat}(n,{\mathbb C})$ and the list of the corresponding invariant subspaces connected with these two matrices is also given. The properties of the corresponding subalgebras are expressed in terms of the graphs associated with the support of the second matrix. For arbitrary $n$ we describe all minimal subsets of the elementary matrices $E_{km}$ that generate the algebra ${\rm Mat}(n,{\mathbb C})$.
dc.description13 pages
dc.identifierhttps://arxiv.org/abs/0807.4696
dc.identifierhttp://arxiv.org/abs/0807.4696
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/172846
dc.subjectRepresentation Theory
dc.subjectGroup Theory
dc.subject20G05 sep (20Cxx, 22E46, 16Gxx)
dc.titleIrreducibility criterion for the set of two matrices
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