Geodesic
On generalized partial twisted smash products
Czechoslovak Mathematical Journal, Tome 64 (2014) no. 3, pp. 767-782
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
DOI : 10.1007/s10587-014-0131-8
Classification : 16S40, 16T05
Keywords: partial bicomodule algebra; partial twisted smash product; partial bicoinvariant; Morita context 
@article{10_1007_s10587_014_0131_8,
     author = {Guo, Shuangjian},
     title = {On generalized partial twisted smash products},
     journal = {Czechoslovak Mathematical Journal},
     pages = {767--782},
     year = {2014},
     volume = {64},
     number = {3},
     doi = {10.1007/s10587-014-0131-8},
     mrnumber = {3298559},
     zbl = {06391524},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10587-014-0131-8/}
}
TY  - JOUR
AU  - Guo, Shuangjian
TI  - On generalized partial twisted smash products
JO  - Czechoslovak Mathematical Journal
PY  - 2014
SP  - 767
EP  - 782
VL  - 64
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.1007/s10587-014-0131-8/
DO  - 10.1007/s10587-014-0131-8
LA  - en
ID  - 10_1007_s10587_014_0131_8
ER  - 
%0 Journal Article
%A Guo, Shuangjian
%T On generalized partial twisted smash products
%J Czechoslovak Mathematical Journal
%D 2014
%P 767-782
%V 64
%N 3
%U http://geodesic.mathdoc.fr/articles/10.1007/s10587-014-0131-8/
%R 10.1007/s10587-014-0131-8
%G en
%F 10_1007_s10587_014_0131_8
Guo, Shuangjian. On generalized partial twisted smash products. Czechoslovak Mathematical Journal, Tome 64 (2014) no. 3, pp. 767-782. doi: 10.1007/s10587-014-0131-8

[1] Alves, M. M. S., Batista, E.: Enveloping actions for partial Hopf actions. Commun. Algebra 38 (2010), 2872-2902. | DOI | MR | Zbl

[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. | DOI | MR | Zbl

[3] Alves, M. M. S., Batista, E.: Partial Hopf actions, partial invariants and a Morita context. Algebra Discrete Math. 2009 (2009), 1-19. | MR | Zbl

[4] Beattie, M., Dăscălescu, S., Raianu, Ş.: Galois extensions for co-Frobenius Hopf algebras. J. Algebra 198 (1997), 164-183. | DOI | MR | Zbl

[5] Caenepeel, S., Janssen, K.: Partial (co)actions of Hopf algebras and partial Hopf-Galois theory. Commun. Algebra 36 (2008), 2923-2946. | DOI | MR | Zbl

[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. | DOI | MR | Zbl

[7] Dokuchaev, M., Ferrero, M., Paques, A.: Partial actions and Galois theory. J. Pure Appl. Algebra 208 (2007), 77-87. | DOI | MR | Zbl

[8] Exel, R.: Circle actions on $C^{*}$-algebras, partial automorphisms, and a generalized Pimsner-Voiculescu exact sequence. J. Funct. Anal. 122 (1994), 361-401. | DOI | MR

[9] Lomp, C.: Duality for partial group actions. Int. Electron. J. Algebra (electronic only) 4 (2008), 53-62. | MR | Zbl

[10] Sweedler, M. E.: Hopf Algebras. Mathematics Lecture Note Series W. A. Benjamin, New York (1969). | MR | Zbl

Cité par Sources :