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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