Reflexive Bimodules
1989 ◽
Vol 41
(4)
◽
pp. 592-611
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Keyword(s):
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.
1982 ◽
Vol 25
(2)
◽
pp. 133-139
◽
1986 ◽
Vol 69
(4)
◽
pp. 37-46
◽
1982 ◽
Vol 86
◽
pp. 229-248
◽
1985 ◽
Vol 28
(3)
◽
pp. 319-331
◽
1985 ◽
Vol 98
◽
pp. 139-156
◽