Geodesic
KERNELS OF REPRESENTATIONS AND COIDEAL SUBALGEBRAS OF HOPF ALGEBRAS
Glasgow mathematical journal, Tome 54 (2012) no. 1, pp. 107-119

Voir la notice de l'article provenant de la source Cambridge University Press

We define left and right kernels of representations of Hopf algebras. In the case of group algebras, left and right kernels coincide and they are the usual kernels of modules. In the general case, we show that these kernels coincide with the categorical left and right Hopf kernels of morphisms of Hopf algebras defined in Andruskiewitsch and Devoto [Extensions of Hopf algebras, Algebra i Analiz7 (1995), 22–69]. Brauer's theorem for kernels over group algebras is generalised to Hopf algebras.
DOI : 10.1017/S0017089511000395
Mots-clés : MSC 16W30 
BURCIU, SEBASTIAN. KERNELS OF REPRESENTATIONS AND COIDEAL SUBALGEBRAS OF HOPF ALGEBRAS. Glasgow mathematical journal, Tome 54 (2012) no. 1, pp. 107-119. doi: 10.1017/S0017089511000395
@article{10_1017_S0017089511000395,
     author = {BURCIU, SEBASTIAN},
     title = {KERNELS {OF} {REPRESENTATIONS} {AND} {COIDEAL} {SUBALGEBRAS} {OF} {HOPF} {ALGEBRAS}},
     journal = {Glasgow mathematical journal},
     pages = {107--119},
     year = {2012},
     volume = {54},
     number = {1},
     doi = {10.1017/S0017089511000395},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089511000395/}
}
TY  - JOUR
AU  - BURCIU, SEBASTIAN
TI  - KERNELS OF REPRESENTATIONS AND COIDEAL SUBALGEBRAS OF HOPF ALGEBRAS
JO  - Glasgow mathematical journal
PY  - 2012
SP  - 107
EP  - 119
VL  - 54
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089511000395/
DO  - 10.1017/S0017089511000395
ID  - 10_1017_S0017089511000395
ER  - 
%0 Journal Article
%A BURCIU, SEBASTIAN
%T KERNELS OF REPRESENTATIONS AND COIDEAL SUBALGEBRAS OF HOPF ALGEBRAS
%J Glasgow mathematical journal
%D 2012
%P 107-119
%V 54
%N 1
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089511000395/
%R 10.1017/S0017089511000395
%F 10_1017_S0017089511000395

[1] 1.Andruskiewitsch, N., Extensions of Hopf algebras, Can. J. Math. 48 (1) (1996), 3–42. Google Scholar | DOI

[2] 2.Andruskiewitsch, N. and Devoto, J., Extensions of Hopf algebras, Algebra i Analiz 7 (1995), 22–69. Google Scholar

[3] 3.Banica, T. and Bichon, J., Hopf images and inner faithful representations, Glasgow Math. J. 52 (2010), 677–703. Google Scholar | DOI

[4] 4.Boltje, R. and Kuelshammer, B., On the depth 2 condition for group algebra and Hopf algebra extensions, J. Algebra 323 (6) (2009), 1783–1796. Google Scholar | DOI

[5] 5.Burciu, S., Normal Hopf subalgebras of semisimple Hopf algebras, Proc. Amer. Math. Soc. 137 (12) (2009), 3969–3979. Google Scholar | DOI

[6] 6.Burciu, S., Kadison, L. and Kuelshammer, B., On subgroup depth, Int. Electron. J. Algebra 9 (2011), 133–166. Google Scholar

[7] 7.Etingof, P. and Gelaki, S., On the exponent of finite dimensional Hopf Algebras, Math. Res. Lett. 6 (2) (1999), 131–140. Google Scholar | DOI

[8] 8.Etingof, P. and Ostrik, V., Finite tensor categories, Moscow J. Math. 4 (3) (2004), 627–654. Google Scholar | DOI

[9] 9.Isaacs, I. M., Character theory of finite groups, in Pure and Applied Mathematics, Vol. 69 (Academic Press, New York/London, 1976). Google Scholar

[10] 10.Masuoka, A., Semisimple Hopf algebras of dimension 2p, Commun. Algebra 23 (5) (1995), 1931–1940. Google Scholar | DOI

[11] 11.Montgomery, S., Hopf algebras and their actions on rings, in CBMS regional conference series in mathematics, Vol. 82 (American Mathematical Society, Providence, RI, 1993). Google Scholar

[12] 12.Passman, D. S. and Quinn, D., Burnside's theorem for Hopf algebras, Proc. Amer. Math. Soc 123 (1995), 327–333. Google Scholar

[13] 13.Rieffel, M., Burnside's theorem for representations of Hopf algebras, J. Algebra 6 (1967), 123–130. Google Scholar | DOI

[14] 14.Rieffel, M., Normal subrings and induced representations, J. Algebra 24 (1979), 264–386. Google Scholar

[15] 15.Skryabin, Y., Projectivity and freeness over comodule algebras, Trans. Amer. Math. Soc 359 (6) (2007), 2597–2623. Google Scholar | DOI

[16] 16.Takeuchi, M., Quotient spaces for Hopf algebras, Commun. Alg. 22 (7) (1995), 2503–2523. Google Scholar | DOI

[17] 17.Waterhouse, W. C., Introduction to affine group schemes, Vol. 69 (Springer-Verlag, Berlin, 1979). Google Scholar | DOI

Cité par Sources :