Inverse semigroupoid actions and representations
DOI:
https://doi.org/10.35819/remat2023v9i1id6174Keywords:
Groupoid, Inverse Semigroupoid, Inverse Semigroupoid Actions, Inverse Semigroupoid RepresentationsAbstract
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 Exel's 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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