RT Journal Article
T1 On the Structure of Finite Groupoids and Their Representations
A1 Ibort Latre, Luis Alberto
A1 Rodriguez, Miguel A.
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
YR 2019
FD 2019-03-20
LK https://hdl.handle.net/10016/38230
UL https://hdl.handle.net/10016/38230
LA eng
NO The authors acknowledge financial support from the Spanish Ministry of Economy and Competitiveness, through the Severo Ochoa Programme for Centres of Excellence in RD (SEV-2015/0554). A.I. would like to thank partial support provided by the MINECO grant MTM2017-84098-P and QUITEMAD++, S2018/TCS-A4342. M.A.R. would like to thank partial financial support from MINECO grant FIS2015-63966-P.
DS e-Archivo
RD 1 sept. 2024