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- Title
Large-$ N $ Limits of Spaces and Structures.
- Authors
Alam, Irfan; Sengupta, Ambar N.
- Abstract
For a sequence of spaces $ X_N $, with topological, algebraic or measure-theoretic structures, we show how a large-$ N $ limit $ X_\infty $ with corresponding structures is obtained. For example, when each space is a topological group $ G_N $, such as $ G_N = U(N) $, a limiting group $ G_\infty $ with topology results. Using the Weil-Kodaira construction, for compact topological groups $ G_N $ equipped with normalized Haar measures, we obtain a topological structure on $ G_\infty $ that also makes the group operations continuous. When each $ G_N $ is a Lie group we describe a Lie algebra associated to $ G_\infty $.
- Subjects
LIE groups; COMPACT groups; TOPOLOGICAL spaces; HAAR integral; CONTINUOUS groups; TOPOLOGICAL groups
- Publication
Communications on Pure & Applied Analysis, 2023, Vol 22, Issue 4, p1
- ISSN
1534-0392
- Publication type
Article
- DOI
10.3934/cpaa.2023019