English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

A notion of factorizable representation is defined and all factorizable representations of a commutative group of functions as well as those of the current commutation relations and canonical commutation relations are explicitly given in the continuous tensor product space (i.e. the Fock space). The formula for a state functional of a factorizable representation is a non-commutative extension of the Levy-Kinchin formula in probability theory. In the course of analysis, the most general form of a first order cocycle of any solvable group with values in a Hilbert space is determined. Non trivial cohomologies appear by two entirely different mechanism, namely a topological one on infinite dimensional space and an algebraic one on a finite dimensional space. The immaginary part of an inner product of such cocycle is a second order cocycle. The condition that it is a coboundary is discussed.

publications of the research institute for mathematical sciences

Factorizable representation of current algebra. Non commutative extension of the Lévy-Kinchin formula and cohomology of a solvable group with values in a Hilbert space