[Top][All Lists]

[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]
## Re: [Axiom-developer] algebras <=> groups

**From**: |
Bertfried Fauser |

**Subject**: |
Re: [Axiom-developer] algebras <=> groups |

**Date**: |
Mon, 14 Jun 2004 20:00:30 +0200 (CEST) |

On 14 Jun 2004, Camm Maguire wrote:
Hi!
>* This having been said, there are two enormous areas of practical*
>* overlap:*
>
>* 1) representation theory -- i.e. the categorization of the eigenspaces*
>* of an operator via its known multiplication rules with the elements*
>* of a 'symmetry' group*
>
>* 2) Lie groups, which are 'generated' by exponentiating the additive*
>* action of an (usually matrix vector) algebra.*
>
>* It would be hard to overstate the significance of being able to*
>* separate eigen solutions of a complex and intractable dynamic operator*
>* from 'symmetry' arguments alone.*
perhaps interesting in this sort of discussion is, that Hopf algebras
unite in some sense these two areas. In a Hopf algebra there are "group
like" elements functioning _exactly_ like a group and so called "primitive
elements" which resemble the algebraic side. However....
ciao
BF.
% PD Dr Bertfried Fauser
% Institution: Max Planck Institut for Mathematics Leipzig
<http://www.mis.mpg.de>
% Privat Docent: University of Konstanz, Physics Dept
<http://www.uni-konstanz.de>
% contact |-> URL : http://clifford.physik.uni-konstanz.de/~fauser/
% Phone : Leipzig +49 341 9959 735 Konstanz +49 7531 693491