Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 2 (2006), 042, 19 pages      math.RT/0602677      http://dx.doi.org/10.3842/SIGMA.2006.042

On Transitive Systems of Subspaces in a Hilbert Space

Yuliya P. Moskaleva a and Yurii S. Samoilenko b
a) Taurida National University, 4 Vernads'kyi Str., Simferopol, 95007 Ukraine
b) Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs'ka Str., Kyiv-4, 01601 Ukraine

Received February 27, 2006; Published online April 12, 2006

Abstract
Methods of *-representations in Hilbert space are applied to study of systems of n subspaces in a linear space. It is proved that the problem of description of n-transitive subspaces in a finite-dimensional linear space is *-wild for n ≥ 5.

Key words: algebras generated by projections; irreducible inequivalent representations; transitive nonisomorphic systems of subspaces.

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