Inverse semigroupoid actions and representations

• Autor(a) principal: Tamusiunas, Thaísa Raupp
• Data de Publicação: 2023
• Outros Autores: Lautenschlaeger, Wesley Gonçalves
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Remat (Bento Gonçalves)
• Texto Completo: https://periodicos.ifrs.edu.br/index.php/REMAT/article/view/6174
• topic: Grupoide; Semigrupoide Inverso; Ações de Semigrupoide Inverso; Representações de Semigrupoide Inverso; Groupoid; Inverse Semigroupoid; Inverse Semigroupoid Actions; Inverse Semigroupoid Representations; Grupoide; Semigrupoide Inverso; Acciones de Semigrupoide Inverso; Representaciones de Semigrupoide Inverso

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.