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A Logarithmic Generalization of Tensor Product Theory for Modules for a Vertex Operator Algebra

Yi-Zhi Huang, James Lepowsky, Lin Zhang

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Abstract

We describe a logarithmic tensor product theory for certain module categories for a "conformal vertex algebra". In this theory, which is a natural, although intricate, generalization of earlier work of Huang and Lepowsky, we do not require the module categories to be semisimple, and we accommodate modules with generalized weight spaces. The corresponding intertwining operators contain logarithms of the variables.

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What this paper is about

We describe a logarithmic tensor product theory for certain module categories for a "conformal vertex algebra". In this theory, which is a natural, although intricate, generalization of earlier work of Huang and Lepowsky, we do not require the module categories to be semisimple, and we accommodate modules with generalized weight spaces. The corresponding intertwining operators contain logarithms of the variables.

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OpenAlex reports 48 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

We describe a logarithmic tensor product theory for certain module categories for a "conformal vertex algebra". In this theory, which is a natural, although intricate, generalization of earlier work of Huang and Lepowsky, we do not require the module categories to be semisimple, and we accommodate modules with generalized weight spaces. The corresponding intertwining operators contain logarithms of the variables.

Key concepts: Mathematics, Tensor product, Tensor product of modules, Vertex operator algebra, Algebra over a field, Logarithm, Generalization, Vertex (graph theory)

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