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Non-singular actions of infinite-dimensional groups and polymorphismsстатья
Статья опубликована в журнале из списка RSCI Web of Science
Статья опубликована в журнале из списка Web of Science и/или Scopus- Автор: Neretin Yu A.
- Журнал: Moscow Mathematical Journal
- Том: 24
- Номер: 3
- Год издания: 2024
- Первая страница: 407
- Последняя страница: 425
- DOI: 10.17323/1609-4514-2024-24-3-407-425
- Аннотация: Let $Z$ be a probability measure space with a measure $\zeta$, $\mathbb{R}^\times$ be the multiplicative group of positive reals, let $t$ be the coordinate on $\mathbb{R}^\times$.A polymorphism of $Z$ is a measure $\pi$ on $Z\times Z\times \mathbb{R}^\times$ such thatfor any measurable $A$, $B\subset Z$ we have $\pi(A\times Z\times \mathbb{R}^\times)=\zeta(A)$ and the integral $\int t\,d\pi(z,u,t)$ over $Z\times B\times \mathbb{R}^\times$ is $\zeta(B)$. The set of all polymorphisms has a natural semigroup structure, the group of all nonsingular transformations is dense in this semigroup. We discuss a problem of closure in polymorphisms for certain types of infinite dimensional ('large') groups and show that a non-singular action of an infinite-dimensional groupgenerates a representation of its train (category of double cosets) by polymorphisms.
- Добавил в систему: Неретин Юрий Александрович