[GAP Forum] How to construct a group algebra by generators using function Algebra(Field, generators) ?

[Laurent Bartholdi]

Dear Dong,
Let me second Alexander's explanation. To define a ring, you must
supply gap with elements that may be added and multiplied. A simple
way to construct ring elements is by converting the permutations to
permutation matrices. The short code

> gap> GroupRing( GF(2), SymmetricGroup(3) );

could have been written as

gap> regularactiongens :=
GeneratorsOfGroup(Action(SymmetricGroup(3),SymmetricGroup(3),OnRight));
[ (1,3,5)(2,4,6), (1,6)(2,5)(3,4) ]
gap> Algebra(GF(2), List(regularactiongens,g->PermutationMat(g,6,GF(2))));
<algebra over GF(2), with 2 generators>

This has the disadvantage that GAP does not know that you constructed
a group ring (and therefore does not know that there is an
augmentation ideal, etc.)

-- 
Laurent Bartholdi          \  laurent.bartholdi<at>gmail<dot>com
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