39.3 FpAlgebra

FpAlgebra( A )

returns a finitely presented algebra isomorphic to the algebra A. At the moment this is implemented only for matrix algebras and finitely presented algebras.

    gap> a:= FreeAlgebra( GF(2), 2 );
    UnitalAlgebra( GF(2), [ a.1, a.2 ] )
    gap> a:= a / [ a.one+a.1^2, a.one+a.2^2, a.one+(a.1*a.2)^3 ];;
    gap> a.name:= "a";; s:= Subalgebra( a, [ a.2 ] );;
    gap> f:= FpAlgebra( s );
    UnitalAlgebra( GF(2), [ a.1 ] )
    gap> PrintDefinitionFpAlgebra( f, "f" );
    f:= FreeAlgebra( GF(2), "a.1" );
    f:= f / [ f.one+f.1^2 ]; 

FpAlgebra( F, fpgroup )

returns the group algebra of the finitely presented group fpgroup over the field F, this is the algebra of formal linear combinations of elements of fpgroup, with coefficients in F; in this case the number of algebra generators is twice the number of group generators, the first half corresponding to the group generators, the second half to their inverses.

    gap> f:= FreeGroup( 2 );;
    gap> s3:= f / [ f.1^2, f.2^2, (f.1*f.2)^3 ];
    Group( f.1, f.2 )
    gap> a:= FpAlgebra( GF(2), s3 );
    UnitalAlgebra( GF(2), [ a.1, a.2, a.3, a.4 ] ) 

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