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Эта публикация цитируется в 1 научной статье (всего в 1 статье)
Linear Representations and Frobenius Morphisms of Groupoids
Juan Jesús Barbarán Sáncheza, Laiachi El Kaoutitba a Universidad de Granada, Departamento de Álgebra, Facultad de Educación, Econonía y Tecnología de Ceuta, Cortadura del Valle, s/n. E-51001 Ceuta, Spain
b IEMath-Granada
Аннотация:
Given a morphism of (small) groupoids with injective object map, we provide sufficient and necessary conditions under which the
induction and co-induction functors between the categories of linear representations are naturally isomorphic. A morphism with
this property is termed a Frobenius morphism of groupoids. As a consequence, an extension by a subgroupoid is Frobenius if and
only if each fibre of the (left or right) pull-back biset has finitely many orbits. Our results extend and clarify the classical Frobenius reciprocity formulae in the theory of finite groups, and characterize Frobenius extension of algebras with enough orthogonal idempotents.
Ключевые слова:
Linear representations of groupoids; restriction, inductions and co-induction functors; groupoids-bisets; translation
groupoids; Frobenius extensions; Frobenius reciprocity formula.
Поступила: 26 июня 2018 г.; в окончательном варианте 22 февраля 2019 г.; опубликована 12 марта 2019 г.
Образец цитирования:
Juan Jesús Barbarán Sánchez, Laiachi El Kaoutit, “Linear Representations and Frobenius Morphisms of Groupoids”, SIGMA, 15 (2019), 019, 33 pp.
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/sigma1455 https://www.mathnet.ru/rus/sigma/v15/p19
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