Geodesic
Hopf algebras of smooth functions on compact Lie groups
Commentationes Mathematicae Universitatis Carolinae, Tome 41 (2000) no. 4, pp. 651-661

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

A $C^{\infty}$-Hopf algebra is a $C^{\infty}$-algebra which is also a convenient Hopf algebra with respect to the structure induced by the evaluations of smooth functions. We characterize those $C^{\infty}$-Hopf algebras which are given by the algebra $C^{\infty}(G)$ of smooth functions on some compact Lie group $G$, thus obtaining an anti-isomorphism of the category of compact Lie groups with a subcategory of convenient Hopf algebras.
Classification : 16W30, 22D35, 22E15, 46E25, 46J15
Keywords: $C^{\infty}$-Hopf-algebras; algebras of smooth functions on compact Lie groups; duality theorem 
@article{CMUC_2000__41_4_a0,
     author = {Farkas, Eva C.},
     title = {Hopf algebras of smooth functions on compact {Lie} groups},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {651--661},
     publisher = {mathdoc},
     volume = {41},
     number = {4},
     year = {2000},
     mrnumber = {1800176},
     zbl = {1051.16021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_2000__41_4_a0/}
}
TY  - JOUR
AU  - Farkas, Eva C.
TI  - Hopf algebras of smooth functions on compact Lie groups
JO  - Commentationes Mathematicae Universitatis Carolinae
PY  - 2000
SP  - 651
EP  - 661
VL  - 41
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMUC_2000__41_4_a0/
LA  - en
ID  - CMUC_2000__41_4_a0
ER  - 
%0 Journal Article
%A Farkas, Eva C.
%T Hopf algebras of smooth functions on compact Lie groups
%J Commentationes Mathematicae Universitatis Carolinae
%D 2000
%P 651-661
%V 41
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMUC_2000__41_4_a0/
%G en
%F CMUC_2000__41_4_a0
Farkas, Eva C. Hopf algebras of smooth functions on compact Lie groups. Commentationes Mathematicae Universitatis Carolinae, Tome 41 (2000) no. 4, pp. 651-661. http://geodesic.mathdoc.fr/item/CMUC_2000__41_4_a0/