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

[Bertfried Fauser]

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
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