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dc.contributor.authorLivshits, L.
dc.contributor.authorMacDonald, G.W.
dc.contributor.authorMarcoux, L.W.
dc.contributor.authorRadjavi, H. 18:36:01 (GMT) 18:36:01 (GMT)
dc.descriptionThis is an Accepted Manuscript of an article published by Taylor & Francis in 'Linear and Multilinear Algebra' on 7/2014, available online:
dc.description.abstractIn this article we verify that ‘Wedderburn’s Principal Theorem’ has a particularly pleasant spatial implementation in the case of cleft subalgebras of the algebra of all linear transformations on a finite-dimensional vector space. Once such a subalgebra A is represented by block upper triangular matrices with respect to a maximal chain of its invariant subspaces, after an application of a block upper triangular similarity, the resulting algebra is a linear direct sum of an algebra of block-diagonal matrices and an algebra of strictly block upper triangular matrices (i.e. the radical), while the block-diagonal matrices involved have a very nice structure. We apply this result to demonstrate that, when the underlying field is algebraically closed, and (Rad(A))μ(A)−1 ≠ {0} the algebra is unicellular, i.e. the lattice of all invariant subspaces of A is totally ordered by inclusion. The quantity μ(A) stands for the length of (every) maximal chain of non-zero invariant subspaces of A.en
dc.description.sponsorshipThe first author was supported by the Colby College Natural Science Division Grant. The second, third and fourth authors acknowledge the support of NSERC Canada.en
dc.publisherTaylor & Francisen
dc.subjectWedderburn's principal theoremen
dc.subjectWedderburn-Artin theoremen
dc.subjectblock-upper-triangular matrix algebrasen
dc.subjectirreducible matrix algebrasen
dc.subjectsemi-simple matrix algebrasen
dc.titleA spatial version of Wedderburn’s Principal Theoremen
dcterms.bibliographicCitationL. Livshits, G.W. MacDonald, L.W. Marcoux & H. Radjavi (2015) A spatial version of Wedderburn’s Principal Theorem, Linear and Multilinear Algebra, 63:6, 1216-1241, DOI: 10.1080/03081087.2014.925452en
uws.contributor.affiliation1Faculty of Mathematicsen
uws.contributor.affiliation2Pure Mathematicsen

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