6 research outputs found
On the Existence of Configurations of Subspaces in a Hilbert Space with Fixed Angles
For a class of -algebras, where -algebra is generated
by projections associated with vertices of graph and depends on a
parameter , we study the sets of
values of such that the algebras have nontrivial
-representations, by using the theory of spectra of graphs. In other words,
we study such values of that the corresponding configurations of
subspaces in a Hilbert space exist.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and
Applications) at http://www.emis.de/journals/SIGMA
On Transitive Systems of Subspaces in a Hilbert Space
Methods of *-representations in Hilbert space are applied to study of systems
of subspaces in a linear space. It is proved that the problem of
description of -transitive subspaces in a finite-dimensional linear space is
*-wild for .Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and
Applications) at http://www.emis.de/journals/SIGMA
On C*-algebras generated by pairs of q-commuting isometries
We consider the C*-algebras O_2^q and A_2^q generated, respectively, by
isometries s_1, s_2 satisfying the relation s_1^* s_2 = q s_2 s_1^* with |q| <
1 (the deformed Cuntz relation), and by isometries s_1, s_2 satisfying the
relation s_2 s_1 = q s_1 s_2 with |q| = 1. We show that O_2^q is isomorphic to
the Cuntz-Toeplitz C*-algebra O_2^0 for any |q| < 1. We further prove that
A_2^{q_1} is isomorphic to A_2^{q_2} if and only if either q_1 = q_2 or q_1 =
complex conjugate of q_2. In the second part of our paper, we discuss the
complexity of the representation theory of A_2^q. We show that A_2^q is *-wild
for any q in the circle |q| = 1, and hence that A_2^q is not nuclear for any q
in the circle.Comment: 18 pages, LaTeX2e "article" document class; submitted. V2 clarifies
the relationships between the various deformation systems treate
On Transitive Systems of Subspaces in a Hilbert Space
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