Topological tensor representations of gl(V) for a space V of countable dimension

2022/06/01 by Francesco Esposito, Esposito, Francesco, Ivan Penkov +1
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Noncommutative and Quantum Gravity Theories #Algebraic structures and combinatorial models

paper · pdf · doi:10.48550/arxiv.2206.00654

Abstract

The Lie algebra gl(V) is the Lie algebra of all endomorphisms of a countable-dimensional complex vector space V. We define a tensor category of topological representations of the Lie algebra gl(V), so that V, its dual and the adjoint representation gl(V) are objects of this category. This makes it an analogue of the category of finite-dimensional modules over the finite-dimensional Lie algebra gl(n). Our main result is that this category is antiequivalent as a symmetric monoidal category to the category of tensor representations of the Lie algebra of finitary infinite matrices.

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