Geodesic
Conditions for the spatial flatness and spatial injectivity of an indecomposable CSL algebra of finite width
Matematičeskie zametki, Tome 63 (1998) no. 1, pp. 9-20

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This paper is concerned with the connection between the geometric properties of the lattice $L$ of subspaces of a Hilbert space $H$ and homological properties (flatness and injectivity) of $H$ regarded as a natural module over the reflexive algebra $\operatorname{Alg}L$ that consists of all operators leaving invariant each element of the lattice $L$. It follows from these results that the cohomology groups with coefficients in $\mathscr B(H)$ are trivial for a broad class of reflexive algebras. 
@article{MZM_1998_63_1_a1,
     author = {Yu. O. Golovin},
     title = {Conditions for the spatial flatness and spatial injectivity of an indecomposable {CSL} algebra of finite width},
     journal = {Matemati\v{c}eskie zametki},
     pages = {9--20},
     publisher = {mathdoc},
     volume = {63},
     number = {1},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1998_63_1_a1/}
}
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Yu. O. Golovin. Conditions for the spatial flatness and spatial injectivity of an indecomposable CSL algebra of finite width. Matematičeskie zametki, Tome 63 (1998) no. 1, pp. 9-20. http://geodesic.mathdoc.fr/item/MZM_1998_63_1_a1/