A new approach to Hom-left-symmetric bialgebras
Czechoslovak Mathematical Journal, Tome 71 (2021) no. 2, pp. 321-333
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

The main purpose of this paper is to consider a new definition of Hom-left-symmetric bialgebra. The coboundary Hom-left-symmetric bialgebra is also studied. In particular, we give a necessary and sufficient condition that $s$-matrix is a solution of the Hom-$S$-equation by a cocycle condition.
The main purpose of this paper is to consider a new definition of Hom-left-symmetric bialgebra. The coboundary Hom-left-symmetric bialgebra is also studied. In particular, we give a necessary and sufficient condition that $s$-matrix is a solution of the Hom-$S$-equation by a cocycle condition.
DOI : 10.21136/CMJ.2021.0238-19
Classification : 17A30, 17B60, 81R12
Keywords: Hom-left-symmetric algebra; Hom-$S$-equation; Hom-left-symmetric bialgebra
@article{10_21136_CMJ_2021_0238_19,
     author = {Sun, Qinxiu and Lou, Qiong and Li, Hongliang},
     title = {A new approach to {Hom-left-symmetric} bialgebras},
     journal = {Czechoslovak Mathematical Journal},
     pages = {321--333},
     year = {2021},
     volume = {71},
     number = {2},
     doi = {10.21136/CMJ.2021.0238-19},
     mrnumber = {4263172},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2021.0238-19/}
}
TY  - JOUR
AU  - Sun, Qinxiu
AU  - Lou, Qiong
AU  - Li, Hongliang
TI  - A new approach to Hom-left-symmetric bialgebras
JO  - Czechoslovak Mathematical Journal
PY  - 2021
SP  - 321
EP  - 333
VL  - 71
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2021.0238-19/
DO  - 10.21136/CMJ.2021.0238-19
LA  - en
ID  - 10_21136_CMJ_2021_0238_19
ER  - 
%0 Journal Article
%A Sun, Qinxiu
%A Lou, Qiong
%A Li, Hongliang
%T A new approach to Hom-left-symmetric bialgebras
%J Czechoslovak Mathematical Journal
%D 2021
%P 321-333
%V 71
%N 2
%U http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2021.0238-19/
%R 10.21136/CMJ.2021.0238-19
%G en
%F 10_21136_CMJ_2021_0238_19
Sun, Qinxiu; Lou, Qiong; Li, Hongliang. A new approach to Hom-left-symmetric bialgebras. Czechoslovak Mathematical Journal, Tome 71 (2021) no. 2, pp. 321-333. doi: 10.21136/CMJ.2021.0238-19

[1] Bai, C.: Left-symmetric bialgebras and an analogue of the classical Yang-Baxter equation. Commun. Contemp. Math. 10 (2008), 221-260. | DOI | MR | JFM

[2] Benayadi, S., Makhlouf, A.: Hom-Lie algebras with symmetric invariant nondegenerate bilinear forms. J. Geom. Phys. 76 (2014), 38-60. | DOI | MR | JFM

[3] Hartwig, J. T., Larsson, D., Silvestrov, S. D.: Deformations of Lie algebras using $\sigma$-derivations. J. Algebra 295 (2006), 314-361. | DOI | MR | JFM

[4] Liu, S., Song, L., Tang, R.: Representations and cohomologies of Hom-pre-Lie algebras. Available at , 18 pages. | arXiv

[5] Makhlouf, A., Silvestrov, S. D.: Hom-algebra structures. J. Gen. Lie Theory Appl. 2 (2008), 51-64. | DOI | MR | JFM

[6] Sheng, Y., Bai, C.: A new approach to Hom-Lie bialgebras. J. Algebra 399 (2014), 232-250. | DOI | MR | JFM

[7] Sheng, Y., Chen, D.: Hom-Lie 2-algebras. J. Algebra 376 (2013), 174-195. | DOI | MR | JFM

[8] Sun, Q., Li, H.: On parakähler Hom-Lie algebras and Hom-left-symmetric bialgebras. Commun. Algebra 45 (2017), 105-120. | DOI | MR | JFM

[9] Yau, D.: The Hom-Yang-Baxter equation, Hom-Lie algebras, and quasi-triangular bialgebras. J. Phys. A, Math. Theor. 42 (2009), Article ID 165202, 12 pages. | DOI | MR | JFM

[10] Yau, D.: Hom-Novikov algebras. J. Phys. A, Math. Theor. 44 (2011), Article ID 085202, 20 pages. | DOI | MR | JFM

[11] Yau, D.: The Hom-Yang-Baxter equation and Hom-Lie algebras. J. Math. Phys. 52 (2011), Article ID 053502, 19 pages. | DOI | MR | JFM

[12] Yau, D.: The classical Hom-Yang-Baxter equation and Hom-Lie bialgebras. Int. Electron. J. Algebra 17 (2015), 11-45. | DOI | MR | JFM

[13] Zhang, R., Hou, D., Bai, C.: A Hom-version of the affinizations of Balinskii-Novikov and Novikov superalgebras. J. Math. Phys. 52 (2011), Article ID 023505, 19 pages. | DOI | MR | JFM

Cité par Sources :