An equivalence between semisimple symmetric Frobenius algebras and Calabi–Yau categories

IF 0.5 4区数学 Journal of Homotopy and Related Structures Pub Date : 2017-05-30 DOI:10.1007/s40062-017-0181-3

Jan Hesse

引用次数: 6

Abstract

We show that the bigroupoid of semisimple symmetric Frobenius algebras over an algebraically closed field and the bigroupoid of Calabi–Yau categories are equivalent. To this end, we construct a trace on the category of finitely-generated representations of a symmetric, semisimple Frobenius algebra, given by the composite of the Frobenius form with the Hattori-Stallings trace.

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半简单对称Frobenius代数与Calabi-Yau范畴之间的等价

证明了代数闭域上半简单对称Frobenius代数的双群似形与Calabi-Yau范畴的双群似形是等价的。为此，我们在对称的半简单Frobenius代数的有限生成表示范畴上构造了一条迹，由Frobenius形式与Hattori-Stallings迹的复合给出。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Journal of Homotopy and Related Structures Mathematics-Geometry and Topology

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期刊介绍： Journal of Homotopy and Related Structures (JHRS) is a fully refereed international journal dealing with homotopy and related structures of mathematical and physical sciences. Journal of Homotopy and Related Structures is intended to publish papers on Homotopy in the broad sense and its related areas like Homological and homotopical algebra, K-theory, topology of manifolds, geometric and categorical structures, homology theories, topological groups and algebras, stable homotopy theory, group actions, algebraic varieties, category theory, cobordism theory, controlled topology, noncommutative geometry, motivic cohomology, differential topology, algebraic geometry.

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