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March 29, 2026Russian Journal of Mathematical Physics0 citations

Continuously Representable Topological Groups with Indecomposable Representations of Bounded Degree

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ASA.I. Shtern

Key Points

  • The aim is to explore conditions under which a topological group can be represented through indecomposable representations.
  • Establish a framework for topological groups and their representations.
  • Analyze families of continuous indecomposable representations in finite-dimensional spaces.
  • Examine the implications of representations of bounded degree.
  • A topological group with the specified representation properties separates its elements.
  • It is proven that such groups are finite extensions of commutative groups with plenty of continuous characters.

Abstract

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

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Cite This Study

A.I. Shtern (2026) studied this question.

synapsesocial.com/papers/69c8c28cde0f0f753b39cea8https://doi.org/10.1134/s1061920826010176
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