Semisimple finite-dimensional Hopf algebras
Sbornik. Mathematics, Tome 198 (2007) no. 9, pp. 1221-1245 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The finite-dimensional semisimple Hopf algebras over an algebraically closed field are classified under the assumption that the algebra has a unique irreducible representation of dimension greater than 1. Bibliography: 9 titles.
@article{SM_2007_198_9_a0,
     author = {V. A. Artamonov},
     title = {Semisimple finite-dimensional {Hopf} algebras},
     journal = {Sbornik. Mathematics},
     pages = {1221--1245},
     year = {2007},
     volume = {198},
     number = {9},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2007_198_9_a0/}
}
TY  - JOUR
AU  - V. A. Artamonov
TI  - Semisimple finite-dimensional Hopf algebras
JO  - Sbornik. Mathematics
PY  - 2007
SP  - 1221
EP  - 1245
VL  - 198
IS  - 9
UR  - http://geodesic.mathdoc.fr/item/SM_2007_198_9_a0/
LA  - en
ID  - SM_2007_198_9_a0
ER  - 
%0 Journal Article
%A V. A. Artamonov
%T Semisimple finite-dimensional Hopf algebras
%J Sbornik. Mathematics
%D 2007
%P 1221-1245
%V 198
%N 9
%U http://geodesic.mathdoc.fr/item/SM_2007_198_9_a0/
%G en
%F SM_2007_198_9_a0
V. A. Artamonov. Semisimple finite-dimensional Hopf algebras. Sbornik. Mathematics, Tome 198 (2007) no. 9, pp. 1221-1245. http://geodesic.mathdoc.fr/item/SM_2007_198_9_a0/

[1] S. Montgomery, Hopf algebras and their actions on rings, Published for the Conference Board of the Mathematical Sciences (University in Chicago, USA, 1992), CBMS Regional Conf. Ser. in Math., 82, Amer. Math. Soc., Providence, RI, 1993 | MR | Zbl

[2] S. Montgomery, “Classifying finite-dimensional semisimple Hopf algebras”, Trends in the representation theory of finite-dimensional algebras (Seattle, WA, 1997), Contemp. Math., 229, Amer. Math. Soc., Providence, RI, 1998, 265–279 | MR | Zbl

[3] R. G. Larson, D. E. Radford, “Finite dimensional cosemisimple Hopf algebras in characteristic 0 are semisimple”, J. Algebra, 117:2 (1988), 267–289 | DOI | MR | Zbl

[4] H.-J. Schneider, Lectures on Hopf algebras, Trab. Mat., 31, Univ. Nacional de Córdoba, Córdoba, 1995 | MR | Zbl

[5] N. Andruskiewitsch, “About finite dimensional Hopf algebras”, Quantum symmetries in theoretical physics and mathematics (Bariloche, 2000), Contemp. Math., 294, Amer. Math. Soc., Providence, RI, 2002, 1–57 | MR

[6] I. M. Isaacs, D. S. Passman, “A characterization of groups in terms of the degrees of their characters”, Pacific J. Math., 15:3 (1965), 877–903 | MR | Zbl

[7] G. Seitz, “Finite groups having only one irreducible representation of degree greater than one”, Proc. Amer. Math. Soc., 19:2 (1968), 459–461 | DOI | MR | Zbl

[8] R. Pirs, Assotsiativnye algebry, Mir, M., 1986 ; R. S. Pierce, Associative algebras, Grad. Texts in Math., 88, Springer-Verlag, New York–Heidelberg–Berlin, 1982 | MR | Zbl | MR | Zbl

[9] Ch. Kertis, I. Rainer, Teoriya predstavlenii konechnykh grupp i assotsiativnykh algebr, Nauka, M., 1969 ; Ch. W. Curtis, I. Reiner, Representation theory of finite groups and associative algebras, Wiley, New York–London, 1962 | MR | MR | Zbl