2019
Том 71
№ 4

All Issues

Podkolzin G. B.

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 (Ukrainian)

Infinitesimal algebras for the hypercomplex system SO(4)//SO(2)

Podkolzin G. B.

Full text (.pdf)

Ukr. Mat. Zh. - 1990. - 42, № 3. - pp. 427–429

Article (Ukrainian)

A group approach to the integration of the infinite Toda chain

Daletskii A. Yu., Podkolzin G. B.

Full text (.pdf)

Ukr. Mat. Zh. - 1988. - 40, № 4. - pp. 518-521