Continuously Irreducibly Representable Groups with Irreducible Representations of Bounded Degree

IF 1.5 3区物理与天体物理 Q2 PHYSICS, MATHEMATICAL

Russian Journal of Mathematical Physics Pub Date : 2025-09-29 DOI:10.1134/S106192082503015X

A.I. Shtern

引用次数: 0

Abstract

We prove that a topological group admitting a family of irreducible unitary representations in Hilbert spaces that separates the elements of the group and whose continuous irreducible representations are finite-dimensional and of bounded degree is a finite extension of a commutative group having sufficiently many continuous characters.

DOI 10.1134/S106192082503015X

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具有有界度不可约表示的连续不可约可表示群

证明了在希尔伯特空间中含有一组不可约酉表示的拓扑群，其连续不可约表示是有限维的有界度的，是具有足够多连续字符的交换群的有限扩展。DOI 10.1134 / S106192082503015X

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来源期刊

Russian Journal of Mathematical Physics 物理-物理：数学物理

CiteScore

3.10

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： Russian Journal of Mathematical Physics is a peer-reviewed periodical that deals with the full range of topics subsumed by that discipline, which lies at the foundation of much of contemporary science. Thus, in addition to mathematical physics per se, the journal coverage includes, but is not limited to, functional analysis, linear and nonlinear partial differential equations, algebras, quantization, quantum field theory, modern differential and algebraic geometry and topology, representations of Lie groups, calculus of variations, asymptotic methods, random process theory, dynamical systems, and control theory.