2019
Том 71
№ 11

All Issues

Chapovsky Yu.

Articles: 5
Article (Russian)

Construction of continuous cocycles for the bicrossed product of locally compact groups

Chapovsky Yu., Podkolzin G. B.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2009. - 61, № 2. - pp. 243-260

For locally compact groups $K, M$, and $N$ such that $M$ and $N$ are subgroups of $K, K = M ∙ N$ and $M ∩ N = \{e\}$, where $e$ is the identity of the group $K$, we give a complete description and propose a method for the construction of pairs of continuous cocycles used in the structure of bicrossed product with cocycles in terms of continuous 2-cocycles on the groups $M, N$, and $$K and 3-cocycles on the group $K$.

Article (Russian)

Finding cocycles in the bicrossed product construction for Lie groups

Chapovsky Yu., Kalyuzhnyi A. A., Podkolzin G. B.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2007. - 59, № 11. - pp. 1510–1522

We find an explicit formula for finding pairs of cocycles for the construction of examples of locally compact quantum groups by using the bicrossed product of Lie groups.

Article (Russian)

Conditional Expectations on Compact Quantum Groups and Quantum Double Cosets

Chapovsky Yu., Kalyuzhnyi A. A., Podkolzin G. B.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2005. - 57, № 5. - pp. 644–653

We prove that a conditional expectation on a compact quantum group that satisfies certain conditions can be decomposed into a composition of two conditional expectations one of which is associated with quantum double cosets and the other preserves the counit.

Article (English)

Factorization of Conditional Expectations on Kac Algebras and Quantum Double Coset Hypergroups

Chapovsky Yu., Kalyuzhnyi A. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2003. - 55, № 12. - pp. 1669-1677

We prove that a conditional expectation on a Kac algebra, under certain conditions, decomposes into a composition of two conditional expectations of a special type and gives rise to a compact quantum hypergroup connected to a quantum Gelfand pair.

Article (English)

Gelfand pair associated with a hoph algebra and a coideal

Chapovsky Yu.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1994. - 46, № 8. - pp. 1055–1066

We consider a pair of a compact quantum group and a coideal in its dual Hopf *-algebra and introduce the notions of Gelfand pair and strict Gelfand pair. For a strict Gelfand pair, we construct two hyper-complex systems dual to each other. As an example, we consider the quantum analog of the pair (U(n), SO(n)).