Inverse Semigroupoid Actions and Representations

2020/07/30 by Wesley G. Lautenschlaeger, Lautenschlaeger, Wesley G., Thaísa Tamusiunas +1
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models

paper · pdf · doi:10.48550/arxiv.2007.15216

Abstract

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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