Ações e representações de semigrupoides inversos

Thaísa Raupp Tamusiunas; Wesley Gonçalves Lautenschlaeger

doi:10.35819/remat2023v9i1id6174

Autores

Thaísa Raupp Tamusiunas Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS, Brasil https://orcid.org/0000-0002-6666-8623
Wesley Gonçalves Lautenschlaeger Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS, Brasil https://orcid.org/0000-0003-3713-5147

DOI:

https://doi.org/10.35819/remat2023v9i1id6174

Palavras-chave:

Grupoide, Semigrupoide Inverso, Ações de Semigrupoide Inverso, Representações de Semigrupoide Inverso

Resumo

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.

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Biografia do Autor

Thaísa Raupp Tamusiunas, Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS, Brasil

http://lattes.cnpq.br/69381335287179622
Wesley Gonçalves Lautenschlaeger, Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS, Brasil

http://lattes.cnpq.br/72288035613464011

Referências

ABADIE, Fernando. On partial actions and groupoids. Proceedings of the American Mathematical Society, v. 132, n. 4, p. 1037-1047, 2004. DOI: https://doi.org/10.1090/S0002-9939-03-07300-3.

BAGIO, Dirceu; FLORES, Daiana; PAQUES, Antonio. Partial actions of ordered groupoids on rings. Journal of Algebra and its Applications, v. 9, n. 3, p. 501-517, 2010. DOI: https://doi.org/10.1142/S021949881000404X.

BAGIO, Dirceu; PAQUES, Antonio. Partial groupoid actions: globalization, Morita theory, and Galois theory. Communications in Algebra, v. 40, n. 10, p. 3658-3678, 2012. DOI: https://doi.org/10.1080/00927872.2011.592889.

BAGIO, Dirceu. Partial actions of inductive groupoids on rings. International Journal of Mathematics, Game Theory, and Algebra, v. 20, n. 3, p. 247, 2011.

BAGIO, Dirceu; PINEDO, Hector. Globalization of partial actions of groupoids on nonunital rings. Journal of Algebra and Its Applications, v. 15, n. 5, p. 1650096, 2016. DOI: https://doi.org/10.1142/S0219498816500961.

BAGIO, Dirceu; PINEDO, Hector. On the separability of the partial skew groupoid ring. São Paulo Journal of Mathematical Sciences, v. 11, n. 2, p. 370-384, 2017. DOI: https://doi.org/10.1007/s40863-017-0068-6.

BUSS, Alcides; MEYER, Ralf. Inverse semigroup actions on groupoids. Rocky Mountain Journal of Mathematics, v. 47, n. 1, p. 53-159, 2017. DOI: https://doi.org/10.1216/RMJ-2017-47-1-53.

CORTES, Wagner. On groupoids and inverse semigroupoids actions. Unpublished manuscript, 2018.

CORTES, Wagner. TAMUSIUNAS, Thaisa. A characterisation for a groupoid Galois extension using partial isomorphisms. Bulletin of the Australian Mathematical Society, v. 96, n. 1, p. 59-68, 2017. DOI: https://doi.org/10.1017/S0004972717000077.

DEWOLF, Darien; PRONK, Dorette. The Ehresmann-Schein-Nambooripad theorem for inverse categories. Theory and Applications of Categories, v. 33, n. 27, p. 813–831, 2018. Available in: http://www.tac.mta.ca/tac/volumes/33/27/33-27.pdf. Accessed in: 15 July 15, 2022.

DOKUCHAEV, Michael; EXEL, Ruy. Associativity of crossed products by partial actions, enveloping actions and partial representations. Transactions of the American Mathematical Society, v. 357, n. 5, p. 1931-1952, 2005. DOI: https://doi.org/10.1090/S0002-9947-04-03519-6.

DOKUCHAEV, Michael. Partial actions: a survey. In: MILIES, César Polcino (Org.). Groups, Algebras and Applications: XVIII Latin American Algebra Colloquium. Contemporary Mathematics, American Mathematical Society, v. 537, p. 173-184, 2011. ISBN 08-2185-239-6.

EXEL, Ruy. Circle actions on C*-algebras, partial automorphisms, and a generalized Pimsner-Voiculescu exact sequence. Journal of Functional Analysis, v. 122, n. 2, p. 361-401, 1994. DOI: https://doi.org/10.1006/jfan.1994.1073.

EXEL, Ruy. Partial actions of groups and actions of inverse semigroups. Proceedings of the American Mathematical Society, v. 126, n. 12, p. 3481-3494, 1998. DOI: https://doi.org/10.1090/S0002-9939-98-04575-4.

EXEL, Ruy; VIEIRA, Felipe. Actions of inverse semigroups arising from partial actions of groups. Journal of mathematical analysis and applications, v. 363, n. 1, p. 86-96, 2010. DOI: https://doi.org/10.1016/j.jmaa.2009.08.001.

GILBERT, Nicholas David. Actions and expansions of ordered groupoids. Journal of Pure and Applied Algebra, v. 198, n. 1-3, p. 175-195, 2003. DOI: https://doi.org/10.1016/j.jpaa.2004.11.006.

KELLENDONK, Johannes; LAWSON, Mark V. Partial actions of groups. International Journal of Algebra and Computation, v. 14, n. 1, p. 87-114, 2004. DOI: https://doi.org/10.1142/S0218196704001657.

LAWSON, Mark; MARGOLIS, Stuart; STEINBERG, Benjamin. Expansions of inverse semigroups. Journal of the Australian Mathematical Society, v. 80, n. 2, p. 205-228, 2006. DOI: https://doi.org/10.1017/S1446788700013082.

LIU, Veny. Free inverse semigroupoids and their inverse subsemigroupoids. Advisor: Jon M. Corson. 2016. Dissertation (Ph.D. in Philosophy in Mathematics) - The University of Alabama, 2016. Available in: https://ir.ua.edu/handle/123456789/2693. Accessed in: 15 July 15, 2022.

RENAULT, Jean. A groupoid approach to C*-algebras. Lecture Notes in Mathematics. v. 793. Berlin: Springer, 1980, 164 p. ISBN 35-4009-977-8.

RENAULT, Jean; SKANDALIS, Georgers. The ideal structure of grupoid crossed product C*-algebras. Journal of Operator Theory, v. 25, n. 1, p. 3-36, 1991. Available in: http://www.jstor.org/stable/24718790. Accessed in: 15 July 15, 2022.