Fwd: [GAP Forum] Can GAP compute indecomposble modules of group algebra KSn?

[Laurent Bartholdi]

Dear Dong,
Yes, this is very easy for GAP. The indecomposable modules are
returned as matrices. Here's a sample computation. For more commands,
try '?Meataxe'.

gap> ks3 := GModuleByMats(List(GeneratorsOfGroup(SymmetricGroup(I3)),x->PermutationMat(x,6,GF(2))),GF(2));;
gap> MTX.Indecomposition(ks3);
[ [ <an immutable 1x6 matrix over GF2>,
      rec( field := GF(2), isMTXModule := true, dimension := 1,
generators := [ <an immutable 1x1 matrix over GF2>,
              <an immutable 1x1 matrix over GF2> ],
basisModuleEndomorphisms := [ <an immutable 1x1 matrix over GF2> ],
          smashMeataxe := rec( endAlgResidue := [ [ [ Z(2)^0 ] ], 1 ],
basisEndoRad := [  ] ), isIndecomposable := true ) ],
  [ <an immutable 1x6 matrix over GF2>,
      rec( field := GF(2), isMTXModule := true, dimension := 1,
generators := [ <an immutable 1x1 matrix over GF2>,
              <an immutable 1x1 matrix over GF2> ],
basisModuleEndomorphisms := [ <an immutable 1x1 matrix over GF2> ],
          smashMeataxe := rec( endAlgResidue := [ [ [ Z(2)^0 ] ], 1 ],
basisEndoRad := [  ] ), isIndecomposable := true ) ],
  [ <an immutable 1x6 matrix over GF2>,
      rec( field := GF(2), isMTXModule := true, dimension := 1,
generators := [ <an immutable 1x1 matrix over GF2>,
              <an immutable 1x1 matrix over GF2> ],
basisModuleEndomorphisms := [ <an immutable 1x1 matrix over GF2> ],
          smashMeataxe := rec( endAlgResidue := [ [ [ Z(2)^0 ] ], 1 ],
basisEndoRad := [  ] ), isIndecomposable := true ) ],
  [ <an immutable 1x6 matrix over GF2>,
      rec( field := GF(2), isMTXModule := true, dimension := 1,
generators := [ <an immutable 1x1 matrix over GF2>,
              <an immutable 1x1 matrix over GF2> ],
basisModuleEndomorphisms := [ <an immutable 1x1 matrix over GF2> ],
          smashMeataxe := rec( endAlgResidue := [ [ [ Z(2)^0 ] ], 1 ],
basisEndoRad := [  ] ), isIndecomposable := true ) ],
  [ <an immutable 2x6 matrix over GF2>,
      rec( field := GF(2), isMTXModule := true, dimension := 2,
generators := [ <an immutable 2x2 matrix over GF2>,
              <an immutable 2x2 matrix over GF2> ],
basisModuleEndomorphisms := [ <an immutable 2x2 matrix over GF2> ],
          smashMeataxe := rec( endAlgResidue := [ <an immutable 2x2
matrix over GF2>, 1 ], basisEndoRad := [  ] ), isIndecomposable :=
true )
     ] ]

On 11/8/07, ¶­¾®³É <dongjc at njau.edu.cn> wrote:
> Hi,
> I am a new man in this field? I have a question:
> Can GAP compute indecomposble modules of group algebra KSn? For example KS3,where K is a finite field with 2 elements.
> Best wishes!
> Dong
>
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum
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>


--
Laurent Bartholdi          \  laurent.bartholdi<at>gmail<dot>com
EPFL SB SMA IMB MAD         \    T¨¦l¨¦phone: +41 21-6935458
Station 8                    \ Secr¨¦taire: +41 21-6935471
CH-1015 Lausanne, Switzerland \      Fax: +41 21-6930339


-- 
Laurent Bartholdi          \  laurent.bartholdi<at>gmail<dot>com
EPFL SB SMA IMB MAD         \    T¨¦l¨¦phone: +41 21-6935458
Station 8                    \ Secr¨¦taire: +41 21-6935471
CH-1015 Lausanne, Switzerland \      Fax: +41 21-6930339