We show a classification method for finite groupoids and discuss the cardinality of cosets and its relation with the index. We prove a generalization of the Lagrange's Theorem and establish a Sylow theory for groupoids.
Provamos que existe uma correspondência um para um entre as ações parciais de um grupoide G sobre um conjunto X e as ações de semigrupoide inverso do semigrupoide inverso de Exel S(G) sobre X. Também definimos representações de semigrupoide inverso sobre um espaço de Hilbert H, bem como a C*-álgebra grupoide parcial de Exel C*_p(G), e provamos que existe uma correspondência um para um entre representações parciais de grupoide de G sobre H, representações de semigrupoide inverso de S(G) sobre H e representações de C*-álgebra de C*_p(G) sobre H.
We show that there is a one-to-one correspondence between the partial actions of a groupoid G on a set X and the inverse semigroupoid actions of the inverse semigroupoid S(G) on X. We also define inverse semigroupoid representations on a Hilbert space H, as well as the Exel's partial groupoid C * -algebra C * p (G), and we prove that there is a one-to-one correspondence between partial groupoid representations of G on H, inverse semigroupoid representations of S(G) on H and C * -algebra representations of C * p (G) on H.
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