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Large-$ N $ Limits of Spaces and Structures

  • *Corresponding author: Ambar N. Sengupta

    *Corresponding author: Ambar N. Sengupta
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  • 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 $.

    Mathematics Subject Classification: Primary: 28E04, 54J05; Secondary: 28C10, 28C20.


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