Linear Representations and Frobenius Morphisms of Groupoids
Barbarán Sánchez, Juan Jesús
El Kaoutit Zerri, Laiachi
Linear representations of groupoids
Inductions and co-induction functors
Translation groupoids
Frobenius extensions
Frobenius reciprocity formula
Restriction
Groupoids-bisets
Given a morphism of (small) groupoids with injective object map, we provide
su cient 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 bre of the (left or right) pull-back biset
has nitely many orbits. Our results extend and clarify the classical Frobenius reciprocity
formulae in the theory of nite groups, and characterize Frobenius extension of algebras
with enough orthogonal idempotents.
2020-01-22T12:05:10Z
2020-01-22T12:05:10Z
2019-03-12
info:eu-repo/semantics/article
Juan Jesús Barbarán Sánchez, Laiachi El Kaoutit, “Linear Representations and Frobenius Morphisms of Groupoids”, SIGMA, 15 (2019), 019, 33 pp.
http://hdl.handle.net/10481/59015
10.3842/SIGMA.2019.019
eng
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
info:eu-repo/semantics/openAccess
Atribución-NoComercial-SinDerivadas 3.0 España
Steklov Mathematical Institute RAS