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Reflexive Bimodules

Published online by Cambridge University Press:  20 November 2018

K. R. Fuller ,
W. K. Nicholson  and
J. F. Watters
K. R. Fuller
Affiliation:
University of Iowa, Iowa City, Iowa
W. K. Nicholson
Affiliation:
University of Calgary, Calgary, Alberta
J. F. Watters
Affiliation:
University of Leicester, Leicester, England
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If VK is a finite dimensional vector space over a field K and L is a lattice of subspaces of V, then, following Halmos [11], alg L is defined to be (the K-algebra of) all K-endomorphisms of V which leave every subspace in L invariant. If R ⊆ end(VK) is any subalgebra we define lat R to be (the sublattice of) all subspaces of VK which are invariant under every transformation in R. Then R ⊆ alg [lat R] and R is called a reflexive algebra when this is equality. Every finite dimensional algebra is isomorphic to a reflexive one ([4]) and these reflexive algebras have been studied by Azoff [1], Barker and Conklin [3] and Habibi and Gustafson [9] among others.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 41 , Issue 4 , 01 August 1989 , pp. 592 - 611
Copyright
Copyright © Canadian Mathematical Society 1989

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