RT Journal Article
T1 On the Structure of Finite Groupoids and Their Representations
A1 Ibort, Alberto
A1 Rodríguez González, Miguel Ángel
AB In this paper, both the structure and the theory of representations of finite groupoids are discussed. A finite connected groupoid turns out to be an extension of the groupoids of pairs of its set of units by its canonical totally disconnected isotropy subgroupoid. An extension of Maschke’s theorem for groups is proved showing that the algebra of a finite groupoid is semisimple and all finite-dimensional linear representations of finite groupoids are completely reducible. The theory of characters for finite-dimensional representations of finite groupoids is developed and it is shown that irreducible representations of the groupoid are in one-to-one correspondence with irreducible representation of its isotropy groups, with an extension of Burnside’s theorem describing the decomposition of the regular representation of a finite groupoid. Some simple examples illustrating these results are exhibited with emphasis on the groupoids interpretation of Schwinger’s description of quantum mechanical systems.
PB MDPI
SN 2073-8994
YR 2019
FD 2019-03-20
LK https://hdl.handle.net/20.500.14352/12541
UL https://hdl.handle.net/20.500.14352/12541
LA eng
NO Ministerio de Economía y Competitividad (MINECO)
NO Centro de Excelencia Severo Ochoa
NO Comunidad de Madrid
DS Docta Complutense
RD 17 abr 2025