Geodesic
The structure of g-digroup actions and representation theory
Algebra and discrete mathematics, Tome 32 (2021) no. 1, pp. 103-126.

Voir la notice de l'article provenant de la source Math-Net.Ru

The aim of this paper is to propose two possible ways of defining a g-digroup action and a first approximation to representation theory of g-digroups.
Keywords: digroups, groups, semigroups, Abelian digroups, symmetric digroups, actions and representations. 
@article{ADM_2021_32_1_a6,
     author = {J. G. Rodr{\'\i}guez-Nieto and O. P. Salazar-D{\'\i}az and R. Vel\'asquez},
     title = {The structure of g-digroup actions and representation theory},
     journal = {Algebra and discrete mathematics},
     pages = {103--126},
     publisher = {mathdoc},
     volume = {32},
     number = {1},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2021_32_1_a6/}
}
TY  - JOUR
AU  - J. G. Rodríguez-Nieto
AU  - O. P. Salazar-Díaz
AU  - R. Velásquez
TI  - The structure of g-digroup actions and representation theory
JO  - Algebra and discrete mathematics
PY  - 2021
SP  - 103
EP  - 126
VL  - 32
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ADM_2021_32_1_a6/
LA  - en
ID  - ADM_2021_32_1_a6
ER  - 
%0 Journal Article
%A J. G. Rodríguez-Nieto
%A O. P. Salazar-Díaz
%A R. Velásquez
%T The structure of g-digroup actions and representation theory
%J Algebra and discrete mathematics
%D 2021
%P 103-126
%V 32
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ADM_2021_32_1_a6/
%G en
%F ADM_2021_32_1_a6
J. G. Rodríguez-Nieto; O. P. Salazar-Díaz; R. Velásquez. The structure of g-digroup actions and representation theory. Algebra and discrete mathematics, Tome 32 (2021) no. 1, pp. 103-126. http://geodesic.mathdoc.fr/item/ADM_2021_32_1_a6/

[1] Soviet Math. Dokl., 6 (1965), 1450–1452 | MR | Zbl

[2] M. Bordemann and F. Wagemann, “Global integration of Leibniz algebras”, Journal of Lie Theory, 27:2 (2017), 555–567 | MR | Zbl

[3] S. Covez, “The local integration of Leibniz algebras”, Annales de l'institut Fourier, 63:1 (2013) | MR | Zbl

[4] R. Felipe, “Digroups and their linear presentations”, East-West J. Math., 8:1 (2006), 27–48 | MR | Zbl

[5] H. Guzmán and F. Ongay, “On the concept of digroup action”, Semigroup Forum, 100 (2020), 461–481 | DOI | MR | Zbl

[6] D. L. Johnson, Presentations of groups, Cambridge University Press, 1997 | MR | Zbl

[7] M. K. Kinyon, “Leibniz algebras, Lie racks, and digroups”, J. Lie Theory, 17:1 (2007), 99–114 | MR | Zbl

[8] K. Liu, A class of group-like objects

[9] J.-L. Loday, “Une version non commutative des algèbres de Lie: les algèbres de Leibniz”, Enseign. Math. (2), 39:3-4 (1993), 269–293 | MR | Zbl

[10] Loday, J.-L., “Dialgebras”, Dialgebras and related operads, Lect. Notes Math., 1763, Springer-Verlag, Berlin, 2001, 7–66 | DOI | MR | Zbl

[11] J. Monterde and F. Ongay, “On integral manifolds for leibniz algebras”, Algebra, 2014 (2014) | DOI

[12] J. Mostovoy, “A comment on the integration of Leibniz algebras”, Comm. Algebra, 41:1 (2013), 185–194 | DOI | MR | Zbl

[13] F. Ongay, “On the notion of digroup”, Comunicaciones del CIMAT, 2010, I-10-04

[14] J. G. Rodríguez-Nieto, O. P. Salazar-Díaz, and R. Velásquez, “Augmented, free and tensor generalized digroups”, Open Mathematics, 17:1 (2019), 71–88 | DOI | MR | Zbl

[15] J. G. Rodríguez-Nieto, O. P. Salazar-Díaz, and R. Velásquez, Sylow-type theorems for generalized digroups, submitted, 2019 | MR

[16] J. G. Rodríguez-Nieto, O. P. Salazar-Díaz, and R. Velásquez, “Abelian and symmetric generalized digroups”, Semigroup Forum, 3 (2021) | MR | Zbl

[17] O. P. Salazar-Díaz, R. Velásquez, and L. A. Wills-Toro, “Generalized digroups”, Communications in Algebra, 44 (2016), 2760–2785 | DOI | MR | Zbl

[18] J. D. H. Smith, “Directional algebras”, Houston Journal of Mathematics, 42:1 (2016), 1–22 | MR | Zbl

[19] A. V. Zhuchok, “Semilattices of subdimonoids”, Asian-European Journal of Mathematics, 4:2 (2011), 359–371 | DOI | MR | Zbl

[20] A. V. Zhuchok, “Free $n$-nilpotent dimonoids”, Algebra Discrete Math., 16:2 (2013), 299–310 | MR | Zbl

[21] A. V. Zhuchok, “Free products of dimonoids”, Quasigroups and Related Systems, 21:2 (2013), 273–278 | MR | Zbl

[22] A. V. Zhuchok and Y. V. Zhuchok, “On two classes of digroups”, Sao Paulo J. Math. Sci., 11 (2017), 240–252 | DOI | MR | Zbl