2019
Том 71
№ 2

All Issues

Popova N. D.

Articles: 3
Article (Ukrainian)

On the *-representation of one class of algebras associated with Coxeter graphs

Popova N. D., Samoilenko Yu. S., Strilets O. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2008. - 60, № 4. - pp. 545–556

We investigate *-representations of a class of algebras that are quotient algebras of the Hecke algebras associated with Coxeter graphs. A description of all unitarily nonequivalent irreducible *-representations of finite-dimensional algebras is given. We prove that only trees that have at most one edge of type s > 3 define algebras of finite Hilbert type for all values of parameters.

Article (Ukrainian)

On the growth of deformations of algebras associated with Coxeter graphs

Popova N. D., Samoilenko Yu. S., Strilets O. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2007. - 59, № 6. - pp. 826–837

We investigate a class of algebras that are deformations of quotient algebras of group algebras of Coxeter groups. For algebras from this class, a linear basis is found by using the “diamond lemma.” A description of all finite-dimensional algebras of this class is given, and the growth of infinite-dimensional algebras is determined.

Article (Russian)

On configurations of subspaces of a Hilbert space with fixed angles between them

Popova N. D., Vlasenko M. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2004. - 56, № 5. - pp. 606–615

We investigate the set of irreducible configurations of subspaces of a Hilbert space for which the angle between every two subspaces is fixed. This is the problem of *-representations of certain algebras generated by idempotents and depending on parameters (on the set of angles). We separate the class of problems of finite and tame representation type. For these problems, we indicate conditions on angles under which the configurations of subspaces exist and describe all irreducible representations.