2019
Том 71
№ 11

All Issues

Popovich S. V.

Articles: 3
Article (Russian)

On Homomorphisms of Algebras Generated by Projectors and Coxeter Functors

Popovich S. V., Samoilenko Yu. S.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2003. - 55, № 9. - pp. 1224-1237

We consider algebras generated by idempotents in Banach spaces and orthoprojectors in Hilbert spaces whose sum is a multiple of the identity. We construct several functors generated by homomorphisms of the algebras considered between categories of representations. We investigate properties of these functors and present their applications.

Article (Ukrainian)

$C*$-Algebras Associated with $F_{2^n }$ Unimodal Dynamical Systems

Maistrenko T. Yu., Popovich S. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2001. - 53, № 7. - pp. 929-938

We consider $C*$-algebras associated with simple unimodal one-dimensional ambiguous dynamical systems $(f,R)$ with certain special restrictions. For these algebras, we present a complete classification of irreducible representations in Hilbert spaces and describe the dual space. As an example, we consider the one-parameter family $f_{μ}(x) = μx(1 − x)$.

Article (Russian)

Radical algebras subgroups of whose adjoint groups are subalgebras

Popovich S. V., Sysak Ya. P.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1997. - 49, № 12. - pp. 1646–1652

We obtain the characteristic for radical algebras subgroups of whose adjoint groups are subalgebras. In particular, we prove that the algebras of this sort are nilpotent with nilpotent length at most three. We give the complete classification of those algebras under consideration which are generated by two elements.