Geodesic
Semisimple Hopf algebras
Čebyševskij sbornik, Tome 15 (2014) no. 1, pp. 19-31.

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

There is given a survey of results on a structure of semisimple finite dimensional Hopf algebras with isomorphic irreducible non-one-dimensional representations. There is found an explicit form of group-like elements in these Hopf algebras and a structure of the dual a Hopf algebra. 
@article{CHEB_2014_15_1_a2,
     author = {V. A. Artamonov},
     title = {Semisimple {Hopf} algebras},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {19--31},
     publisher = {mathdoc},
     volume = {15},
     number = {1},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2014_15_1_a2/}
}
TY  - JOUR
AU  - V. A. Artamonov
TI  - Semisimple Hopf algebras
JO  - Čebyševskij sbornik
PY  - 2014
SP  - 19
EP  - 31
VL  - 15
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CHEB_2014_15_1_a2/
LA  - ru
ID  - CHEB_2014_15_1_a2
ER  - 
%0 Journal Article
%A V. A. Artamonov
%T Semisimple Hopf algebras
%J Čebyševskij sbornik
%D 2014
%P 19-31
%V 15
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CHEB_2014_15_1_a2/
%G ru
%F CHEB_2014_15_1_a2
V. A. Artamonov. Semisimple Hopf algebras. Čebyševskij sbornik, Tome 15 (2014) no. 1, pp. 19-31. http://geodesic.mathdoc.fr/item/CHEB_2014_15_1_a2/

[1] V. A. Artamonov, “Poluprostye algebry Khopfa s ogranicheniyami na neprivodimye neodnomernye moduli”, Algebra i analiz, 26:2 (2014)

[2] V. A. Artamonov, “On semisimple Hopf algebras with few representations of dimension greater than one”, Revista de la Unión Matemática Argentina, 51:2 (2010), 91–105 | MR | Zbl

[3] Mukhatov R. B., O strukture poluprostykh algebr Khopfa, Rukopis. Dep. v VINITI 17.10.2012, No 405-V2012

[4] V. A. Artamonov, I. A. Chubarov, “Dual algebras of some semisimple finite dimensional Hopf algebras”, Modules and comodules, Trends in Mathematics, Birkhauser Verlag, Basel, 2008, 65–85 | DOI | MR | Zbl

[5] V. A. Artamonov, I. A. Chubarov, “Properties of some semisimple Hopf algebras”, Algebras, representations and applications, A conference in honour of Ivan Shestakov's 60th birthday (August 26–September 1, 2007, Maresias, Brazil), Contemp. Math., 483, eds. Vyacheslav Futorny, Victor Kac, Iryna Kashuba, E. Zelmanov, Amer. Math. Soc., 2009, 23–36 | DOI | MR | Zbl

[6] Tambara D., Yamagami S., “Tensor Categories with Fusion Rules of Self-Duality for Finite Abelian Groups”, J. Algebra, 209 (1998), 692–707 | DOI | MR | Zbl

[7] A. Masuoka, “Some further classification results on semisimple Hopf algebras”, Commun. Algebra, 24 (1996), 307–329 | DOI | MR | Zbl

[8] S. Natale, “Semisolvability of semisimple Hopf algebras of low dimension”, Memoirs of AMS, 186, 2007 | DOI | MR

[9] Sonia Natale, Julia Yael Plavnik, “On fusion categories with few irreducible degrees”, Algebra and Number theory, 6:6 (2012), 1171–1197 | DOI | MR | Zbl

[10] Frucht R., “Über die Darstekkung endlicher abeischer Gruppen durch Kollineationen”, J. reine angew. Math., 166 (1932), 16–29

[11] E. G. Puninskii, “Gruppovye elementy nekotorykh poluprostykh konechnomernykh algebr Khopfa”, Vestnik MGU. Ser. 1, Matematika. Mekhanika, 2010, no. 5, 15–20 | MR

[12] Spiridonova S. Yu., “O nekotorykh poluprostykh algebrakh Khopfa razmernosti $n(n+1)$”, Matematicheskie zametki, 91:2 (2012), 253–269 | DOI | Zbl

[13] Spiridonova S. Yu., “Obobschennaya kokommutativnost nekotorykh algebr Khopfa i ikh svyaz s konechnymi polyami”, Algebra i analiz, 25:5 (2013), 253–269