| Title:
|
On generalized partial twisted smash products (English) |
| Author:
|
Guo, Shuangjian |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
64 |
| Issue:
|
3 |
| Year:
|
2014 |
| Pages:
|
767-782 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We first introduce the notion of a right generalized partial smash product and explore some properties of such partial smash product, and consider some examples. Furthermore, we introduce the notion of a generalized partial twisted smash product and discuss a necessary condition under which such partial smash product forms a Hopf algebra. Based on these notions and properties, we construct a Morita context for partial coactions of a co-Frobenius Hopf algebra. (English) |
| Keyword:
|
partial bicomodule algebra |
| Keyword:
|
partial twisted smash product |
| Keyword:
|
partial bicoinvariant |
| Keyword:
|
Morita context |
| MSC:
|
16S40 |
| MSC:
|
16T05 |
| idZBL:
|
Zbl 06391524 |
| idMR:
|
MR3298559 |
| DOI:
|
10.1007/s10587-014-0131-8 |
| . |
| Date available:
|
2014-12-19T16:10:50Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144057 |
| . |
| Reference:
|
[1] Alves, M. M. S., Batista, E.: Enveloping actions for partial Hopf actions.Commun. Algebra 38 (2010), 2872-2902. Zbl 1226.16022, MR 2730285, 10.1080/00927870903095582 |
| Reference:
|
[2] Alves, M. M. S., Batista, E.: Globalization theorems for partial Hopf (co)actions, and some of their applications.Groups, Algebras and Applications. Proceedings of XVIII Latin American algebra colloquium, São Pedro, Brazil, 2009 C. Polcino Milies Contemporary Mathematics 537 American Mathematical Society, Providence (2011), 13-30. Zbl 1232.16020, MR 2799089, 10.1090/conm/537/10564 |
| Reference:
|
[3] Alves, M. M. S., Batista, E.: Partial Hopf actions, partial invariants and a Morita context.Algebra Discrete Math. 2009 (2009), 1-19. Zbl 1199.16059, MR 2640384 |
| Reference:
|
[4] Beattie, M., Dăscălescu, S., Raianu, Ş.: Galois extensions for co-Frobenius Hopf algebras.J. Algebra 198 (1997), 164-183. Zbl 0901.16017, MR 1482980, 10.1006/jabr.1997.7146 |
| Reference:
|
[5] Caenepeel, S., Janssen, K.: Partial (co)actions of Hopf algebras and partial Hopf-Galois theory.Commun. Algebra 36 (2008), 2923-2946. Zbl 1168.16021, MR 2440292, 10.1080/00927870802110334 |
| Reference:
|
[6] Dokuchaev, M., Exel, R.: Associativity of crossed products by partial actions, enveloping actions and partial representations.Trans. Am. Math. Soc. 357 (2005), 1931-1952. Zbl 1072.16025, MR 2115083, 10.1090/S0002-9947-04-03519-6 |
| Reference:
|
[7] Dokuchaev, M., Ferrero, M., Paques, A.: Partial actions and Galois theory.J. Pure Appl. Algebra 208 (2007), 77-87. Zbl 1142.13005, MR 2269829, 10.1016/j.jpaa.2005.11.009 |
| Reference:
|
[8] Exel, R.: Circle actions on $C^{*}$-algebras, partial automorphisms, and a generalized Pimsner-Voiculescu exact sequence.J. Funct. Anal. 122 (1994), 361-401. MR 1276163, 10.1006/jfan.1994.1073 |
| Reference:
|
[9] Lomp, C.: Duality for partial group actions.Int. Electron. J. Algebra (electronic only) 4 (2008), 53-62. Zbl 1175.16020, MR 2417468 |
| Reference:
|
[10] Sweedler, M. E.: Hopf Algebras.Mathematics Lecture Note Series W. A. Benjamin, New York (1969). Zbl 0203.31601, MR 0252485 |
| . |
