Residually linear abstract groupoids

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Аннотация

We introduce the notion of residually linear groupoids. We characterize this class in analogy with the group-theoretic setting. Various properties are proved and a relationship with residual finiteness is investigated. From a categorical point of view, our approach extends some well-known results in the theory of discrete groups, due mainly to Mal'cev and Menal. Finally, as an application, we show that the character groupoid of the Hopf algebroid of representative functions of a transitive groupoid is always residually linear.Bibliography: 24 titles.

Авторлар туралы

Khalid Draoui

Sidi Mohamed Ben Abdellah University

Хат алмасуға жауапты Автор.
Email: khalid.draoui@usmba.ac.ma
ORCID iD: 0000-0001-9879-4096

PhD, no status

Hanan Choulli

Sidi Mohamed Ben Abdellah University

Email: hanan.choulli@usmba.ac.ma

Doctor of Science, Professor

Hakima Mouanis

Sidi Mohamed Ben Abdellah University

Email: hakima.mouanis@usmba.ac.ma

Әдебиет тізімі

  1. R. Brown, “From groups to groupoids: a brief survey”, Bull. London Math. Soc., 19:2 (1987), 113–134
  2. H. Brandt, “Über eine Verallgemeinerung des Gruppenbegriffes”, Math. Ann., 96:1 (1927), 360–366
  3. P. J. Higgins, Notes on categories and groupoids, Van Nostrand Rienhold Math. Stud., 32, Van Nostrand Reinhold Co., London–New York–Melbourne, 1971, v+178 pp.
  4. C. Ehresmann, “Gattungen von lokalen Strukturen”, Jber. Deutsch. Math.-Verein., 60 (1957), 49–77
  5. J. J. Barbaran Sanchez, L. El Kaoutit, “Linear representations and Frobenius morphisms of groupoids”, SIGMA, 15 (2019), 019, 33 pp.
  6. K. W. Gruenberg, “Residual properties of infinite soluble groups”, Proc. London Math. Soc. (3), 7 (1957), 29–62
  7. А. Мальцев, “Об изоморфном представлении бесконечных групп матрицами”, Матем. сб., 8(50):3 (1940), 405–422
  8. W. Magnus, “Residually finite groups”, Bull. Amer. Math. Soc., 75 (1969), 305–316
  9. D. Segal, “Residually finite groups”, Groups–Canberra 1989, Lecture Notes in Math., 1456, Springer-Verlag, Berlin, 1990, 85–95
  10. P. Menal, “Residual linearity for certain nilpotent groups”, Proc. Amer. Math. Soc., 68:1 (1978), 27–31
  11. A. Robert, Introduction to the representation theory of compact and locally compact groups, London Math. Soc. Lecture Note Ser., 80, Cambridge Univ. Press, Cambridge–New York, 1983, ix+205 pp.
  12. A. Joyal, R. Street, “An introduction to Tannaka duality and quantum groups”, Category theory (Como, 1990), Lecture Notes in Math., 1488, Springer-Verlag, Berlin, 1991, 413–492
  13. H. Choulli, K. Draoui, H. Mouanis, “Residually linear groups”, Proc. Jangjeon Math. Soc., 27:2 (2024), 271–288
  14. M. Amini, “Tannak–Krein duality for compact groupoids II, duality”, Oper. Matrices, 4:4 (2010), 573–592
  15. С. Маклейн, Категории для работающего математика, Физматлит, М., 2004, 352 с.
  16. E. Abe, Hopf algebras, Transl. from the Japan., Cambridge Tracts in Math., 74, Cambridge Univ. Press, Cambridge–New York, 1980, xii+284 pp.
  17. H.-J. Baues, M. Jibladze, “Classification of Abelian track categories”, $K$-theory, 25:3 (2002), 299–311
  18. A. Paques, T. Tamusiunas, “The Galois correspondence theorem for groupoid actions”, J. Algebra, 509 (2018), 105–123
  19. F. Komura, “Quotients of Etale groupoids and the abelianizations of groupoid $C^*$-algebras”, J. Aust. Math. Soc., 111:1 (2021), 56–75
  20. L. El Kaoutit, L. Spinosa, “On Burnside theory for groupoids”, Bull. Math. Soc. Sci. Math. Roumanie (N.S.), 66(114):1 (2023), 41–87
  21. L. El Kaoutit, Representative functions on discrete groupoids and duality with Hopf algebroids, 2013
  22. L. El Kaoutit, “On geometrically transitive Hopf algebroids”, J. Pure Appl. Algebra, 222:11 (2018), 3483–3520
  23. L. El Kaoutit, J. Gomez-Torrecillas, “On the finite dual of a cocommutative Hopf algebroid. Application to linear differential matrix equations and Picard–Vessiot theory”, Bull. Belg. Math. Soc. Simon Stevin, 28:1 (2021), 53–121
  24. A. J. Berrick, “Groups with no nontrivial linear representations”, Bull. Aust. Math. Soc., 50:1 (1994), 1–11

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© Draoui K., Choulli H., Mouanis H., 2024

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