| Title:
|
A new approach to Hom-left-symmetric bialgebras (English) |
| Author:
|
Sun, Qinxiu |
| Author:
|
Lou, Qiong |
| Author:
|
Li, Hongliang |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
71 |
| Issue:
|
2 |
| Year:
|
2021 |
| Pages:
|
321-333 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Hom-left-symmetric algebra |
| Keyword:
|
Hom-$S$-equation |
| Keyword:
|
Hom-left-symmetric bialgebra |
| MSC:
|
17A30 |
| MSC:
|
17B60 |
| MSC:
|
81R12 |
| idZBL:
|
07361071 |
| idMR:
|
MR4263172 |
| DOI:
|
10.21136/CMJ.2021.0238-19 |
| . |
| Date available:
|
2021-05-20T13:39:27Z |
| Last updated:
|
2023-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148907 |
| . |
| Reference:
|
[1] Bai, C.: Left-symmetric bialgebras and an analogue of the classical Yang-Baxter equation.Commun. Contemp. Math. 10 (2008), 221-260. Zbl 1173.17025, MR 2409367, 10.1142/S0219199708002752 |
| Reference:
|
[2] Benayadi, S., Makhlouf, A.: Hom-Lie algebras with symmetric invariant nondegenerate bilinear forms.J. Geom. Phys. 76 (2014), 38-60. Zbl 1331.17028, MR 3144357, 10.1016/j.geomphys.2013.10.010 |
| Reference:
|
[3] Hartwig, J. T., Larsson, D., Silvestrov, S. D.: Deformations of Lie algebras using $\sigma$-derivations.J. Algebra 295 (2006), 314-361. Zbl 1138.17012, MR 2194957, 10.1016/j.jalgebra.2005.07.036 |
| Reference:
|
[4] Liu, S., Song, L., Tang, R.: Representations and cohomologies of Hom-pre-Lie algebras.Available at https://arxiv.org/abs/1902.07360v1 (2019), 18 pages. |
| Reference:
|
[5] Makhlouf, A., Silvestrov, S. D.: Hom-algebra structures.J. Gen. Lie Theory Appl. 2 (2008), 51-64. Zbl 1184.17002, MR 2399415, 10.4303/jglta/S070206 |
| Reference:
|
[6] Sheng, Y., Bai, C.: A new approach to Hom-Lie bialgebras.J. Algebra 399 (2014), 232-250. Zbl 1345.17002, MR 3144586, 10.1016/j.jalgebra.2013.08.046 |
| Reference:
|
[7] Sheng, Y., Chen, D.: Hom-Lie 2-algebras.J. Algebra 376 (2013), 174-195. Zbl 1281.17034, MR 3003723, 10.1016/j.jalgebra.2012.11.032 |
| Reference:
|
[8] Sun, Q., Li, H.: On parakähler Hom-Lie algebras and Hom-left-symmetric bialgebras.Commun. Algebra 45 (2017), 105-120. Zbl 1418.17068, MR 3556559, 10.1080/00927872.2016.1175453 |
| Reference:
|
[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. Zbl 1179.17001, MR 2539278, 10.1088/1751-8113/42/16/165202 |
| Reference:
|
[10] Yau, D.: Hom-Novikov algebras.J. Phys. A, Math. Theor. 44 (2011), Article ID 085202, 20 pages. Zbl 1208.81110, MR 2770370, 10.1088/1751-8113/44/8/085202 |
| Reference:
|
[11] Yau, D.: The Hom-Yang-Baxter equation and Hom-Lie algebras.J. Math. Phys. 52 (2011), Article ID 053502, 19 pages. Zbl 1317.16032, MR 2839083, 10.1063/1.3571970 |
| Reference:
|
[12] Yau, D.: The classical Hom-Yang-Baxter equation and Hom-Lie bialgebras.Int. Electron. J. Algebra 17 (2015), 11-45. Zbl 1323.16027, MR 3310684, 10.24330/ieja.266210 |
| Reference:
|
[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. Zbl 1314.17007, MR 2798403, 10.1063/1.3546025 |
| . |
