Hopf algebras of smooth functions on compact Lie groups

Eva C. Farkas

Commentationes Mathematicae Universitatis Carolinae (2000)

  • Volume: 41, Issue: 4, page 651-661
  • ISSN: 0010-2628

Abstract

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A C ∞ -Hopf algebra is a C ∞ -algebra which is also a convenient Hopf algebra with respect to the structure induced by the evaluations of smooth functions. We characterize those C ∞ -Hopf algebras which are given by the algebra C ∞ ( 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.

How to cite

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Farkas, Eva C.. "Hopf algebras of smooth functions on compact Lie groups." Commentationes Mathematicae Universitatis Carolinae 41.4 (2000): 651-661. <http://eudml.org/doc/248603>.

@article{Farkas2000,
abstract = {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.},
author = {Farkas, Eva C.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {$C^\{\infty \}$-Hopf-algebras; algebras of smooth functions on compact Lie groups; duality theorem; -Hopf algebras; compact Lie groups; dualities; categories of Hopf algebras},
language = {eng},
number = {4},
pages = {651-661},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Hopf algebras of smooth functions on compact Lie groups},
url = {http://eudml.org/doc/248603},
volume = {41},
year = {2000},
}

TY - JOUR
AU - Farkas, Eva C.
TI - Hopf algebras of smooth functions on compact Lie groups
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2000
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 41
IS - 4
SP - 651
EP - 661
AB - 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.
LA - eng
KW - $C^{\infty }$-Hopf-algebras; algebras of smooth functions on compact Lie groups; duality theorem; -Hopf algebras; compact Lie groups; dualities; categories of Hopf algebras
UR - http://eudml.org/doc/248603
ER -

References

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