Mathematics Branches, Topics, and Sub-Topics

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22Bxx Locally compact abelian groups

This subtopic studies locally compact abelian groups, focusing on harmonic analysis, Pontryagin duality, and structural classification in the locally compact setting.

Specific topics

22B05 General properties and structure of LCA groups

Overview

22B05 studies general properties and structure of lca groups in locally compact abelian groups. It studies harmonic-analytic and structural properties of locally compact abelian groups, with emphasis on duality and decomposition.

Related Wikipedia Page

Locally Compact Abelian Groups (Wikipedia)

Useful Links

Key Ideas

  • Canonical formulations and representative examples for general properties and structure of lca groups
  • How structural, local, and computational viewpoints interact in the subject
  • Standard theorem patterns and invariants used in current research practice

Typical Uses

Used in harmonic analysis, Pontryagin duality, and the structure theory of topological abelian groups.

Applications

  • Pontryagin duality
  • Harmonic analysis on LCA groups
  • Structure and decomposition

References

Recommended Textbooks

22B10 Structure of group algebras of LCA groups

Overview

22B10 studies structure of group algebras of lca groups in locally compact abelian groups. It studies harmonic-analytic and structural properties of locally compact abelian groups, with emphasis on duality and decomposition.

Related Wikipedia Page

Locally Compact Abelian Groups (Wikipedia)

Useful Links

Key Ideas

  • Canonical formulations and representative examples for structure of group algebras of lca groups
  • How structural, local, and computational viewpoints interact in the subject
  • Standard theorem patterns and invariants used in current research practice

Typical Uses

Used in harmonic analysis, Pontryagin duality, and the structure theory of topological abelian groups.

Applications

  • Pontryagin duality
  • Harmonic analysis on LCA groups
  • Structure and decomposition

References

Recommended Textbooks