非半单模块类别的扩展TQFT

IF 1.2 2区数学 Q1 MATHEMATICS

Indiana University Mathematics Journal Pub Date : 2021-03-08 DOI:10.1512/iumj.2021.70.9364

M. Renzi

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引用次数: 4

摘要

我们从（可能是非半单的）模范畴中构造了三维一度扩展拓扑量子场论（简称ETQFT），并在它们的图像中明确地识别了线性范畴和函子。由我们的构造产生的ETQFT的圆范畴等价于底层模范畴的投影对象的全子范畴。特别是，它不必是半单的。

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Extended TQFTs from non-semisimple modular categories

We construct 3-dimensional once-Extended Topological Quantum Field Theories (ETQFTs for short) out of (possibly non-semisimple) modular categories, and we explicitly identify linear categories and functors in their image. The circle category of an ETQFT produced by our construction is equivalent to the full subcategory of projective objects of the underlying modular category. In particular, it need not be semisimple.

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