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Chris Wensley
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May 11, 2021
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,47 @@ | ||
| #4481, issue reported by Chris Wensley | ||
| gap> G := Group( (1,2,3,4,5) );; | ||
| gap> F := GF(3);; | ||
| gap> A := GroupRing( F, G );; | ||
| gap> vecA := BasisVectors( Basis( A ) );; | ||
| gap> AI := AugmentationIdeal( A );; | ||
| gap> vecI := BasisVectors( Basis( AI ) );; | ||
| gap> maps := ListWithIdenticalEntries( 5, 0 );; | ||
| gap> for j in [1..5] do | ||
| > im := List( vecI, v -> v*vecA[j] ); | ||
| > maps[j] := LeftModuleHomomorphismByImages( AI, AI, vecI, im ); | ||
| > od; | ||
| gap> M := Algebra( F, maps );; | ||
| gap> hom := LeftModuleHomomorphismByImages( A, M, vecA, maps ); | ||
| [ (Z(3)^0)*(), (Z(3)^0)*(1,2,3,4,5), (Z(3)^0)*(1,3,5,2,4), | ||
| (Z(3)^0)*(1,4,2,5,3), (Z(3)^0)*(1,5,4,3,2) ] -> | ||
| [ [ (Z(3)^0)*()+(Z(3))*(1,2,3,4,5), (Z(3)^0)*(1,2,3,4,5)+(Z(3))*(1,3,5,2,4), | ||
| (Z(3)^0)*(1,3,5,2,4)+(Z(3))*(1,4,2,5,3), | ||
| (Z(3)^0)*(1,4,2,5,3)+(Z(3))*(1,5,4,3,2) ] -> | ||
| [ (Z(3)^0)*()+(Z(3))*(1,2,3,4,5), (Z(3)^0)*(1,2,3,4,5)+(Z(3))*(1,3,5,2,4), | ||
| (Z(3)^0)*(1,3,5,2,4)+(Z(3))*(1,4,2,5,3), | ||
| (Z(3)^0)*(1,4,2,5,3)+(Z(3))*(1,5,4,3,2) ], | ||
| [ (Z(3)^0)*()+(Z(3))*(1,2,3,4,5), (Z(3)^0)*(1,2,3,4,5)+(Z(3))*(1,3,5,2,4), | ||
| (Z(3)^0)*(1,3,5,2,4)+(Z(3))*(1,4,2,5,3), | ||
| (Z(3)^0)*(1,4,2,5,3)+(Z(3))*(1,5,4,3,2) ] -> | ||
| [ (Z(3)^0)*(1,2,3,4,5)+(Z(3))*(1,3,5,2,4), | ||
| (Z(3)^0)*(1,3,5,2,4)+(Z(3))*(1,4,2,5,3), | ||
| (Z(3)^0)*(1,4,2,5,3)+(Z(3))*(1,5,4,3,2), (Z(3))*()+(Z(3)^0)*(1,5,4,3,2) | ||
| ], | ||
| [ (Z(3)^0)*()+(Z(3))*(1,2,3,4,5), (Z(3)^0)*(1,2,3,4,5)+(Z(3))*(1,3,5,2,4), | ||
| (Z(3)^0)*(1,3,5,2,4)+(Z(3))*(1,4,2,5,3), | ||
| (Z(3)^0)*(1,4,2,5,3)+(Z(3))*(1,5,4,3,2) ] -> | ||
| [ (Z(3)^0)*(1,3,5,2,4)+(Z(3))*(1,4,2,5,3), | ||
| (Z(3)^0)*(1,4,2,5,3)+(Z(3))*(1,5,4,3,2), (Z(3))*()+(Z(3)^0)*(1,5,4,3,2), | ||
| (Z(3)^0)*()+(Z(3))*(1,2,3,4,5) ], | ||
| [ (Z(3)^0)*()+(Z(3))*(1,2,3,4,5), (Z(3)^0)*(1,2,3,4,5)+(Z(3))*(1,3,5,2,4), | ||
| (Z(3)^0)*(1,3,5,2,4)+(Z(3))*(1,4,2,5,3), | ||
| (Z(3)^0)*(1,4,2,5,3)+(Z(3))*(1,5,4,3,2) ] -> | ||
| [ (Z(3)^0)*(1,4,2,5,3)+(Z(3))*(1,5,4,3,2), (Z(3))*()+(Z(3)^0)*(1,5,4,3,2), | ||
| (Z(3)^0)*()+(Z(3))*(1,2,3,4,5), (Z(3)^0)*(1,2,3,4,5)+(Z(3))*(1,3,5,2,4) | ||
| ], | ||
| [ (Z(3)^0)*()+(Z(3))*(1,2,3,4,5), (Z(3)^0)*(1,2,3,4,5)+(Z(3))*(1,3,5,2,4), | ||
| (Z(3)^0)*(1,3,5,2,4)+(Z(3))*(1,4,2,5,3), | ||
| (Z(3)^0)*(1,4,2,5,3)+(Z(3))*(1,5,4,3,2) ] -> | ||
| [ (Z(3))*()+(Z(3)^0)*(1,5,4,3,2), (Z(3)^0)*()+(Z(3))*(1,2,3,4,5), | ||
| (Z(3)^0)*(1,2,3,4,5)+(Z(3))*(1,3,5,2,4), | ||
| (Z(3)^0)*(1,3,5,2,4)+(Z(3))*(1,4,2,5,3) ] ] |