[GAP Forum] Automorphism of Algebra

[Willem De Graaf]

Dear Alper Odabaş,

Currently GAP does not have much functionality for working
with automorphisms of algebras. However, there are functions
for constructing homomorphisms (which, as a special case,
can be automorphisms). This is done by using the function
"AlgebraHomomorphismByImages".
The GAP manual contains a description of this function,
it is available online:
http://www.gap-system.org/Manuals/doc/htm/ref/CHAP060.htm#SECT009

(Note that in order to use it, one must specify  set of source generators,
and a set of image generators.)

Best wishes,

Willem de Graaf


Alper Odabaş wrote:

>Hi all,
>
>I have a question for algebra ,
>Let A and B algebras. Suppose that B acts on A, is there a algebra homomorphism B --> Aut(A) ?? 
>
>has GAP any function Automorphism of commutative algebras??
>
>gap> G:=Group((1,2,3,4));;
>gap> A:=GroupRing(GF(3),G);;
>gap> Automorphism(A);
>Variable: 'Automorphism' must have a value
>
>gap> AutomorphismAlgebra(A);
>Variable: 'AutomorphismAlgebra' must have a value
>
>gap> Automorphisms(A);
>Variable: 'Automorphisms' must have a value
>
>gap> Automorphism(A);
>Variable: 'Automorphism' must have a value
>
>gap> AutomorphismOfAlgebra(A);
>Variable: 'AutomorphismOfAlgebra' must have a value
>
>gap> AutomorphismRing(A);
>Variable: 'AutomorphismRing' must have a value
>
>gap> AutomorphismOfRing(A);
>Variable: 'AutomorphismOfRing' must have a value
>
>
>thanks.
>
>Alper
> 
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