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GradedLieAlgebras :: symmCyclePermLie

symmCyclePermLie -- checks if a permutation of the generators in the form of cycles is an automorphism

Synopsis

Description

Input is a permutation of the generators given as a list of cycles. Output is either an error message or the automorphism. The Lie algebra in the exampel below is called the "Opera" case and is taken from the article by Löfwall-Roos cited on the title page.

i1 : L=lieAlgebra({0,1,2,3,4},{[0,0],[0,1],[0,2],
        {{1,-1},{[1,2],[0,3]}},{{1,2},{[2,2],[1,3]}},
         {{1,2},{[2,2],[0,4]}},{{1,-1},{[2,3],[1,4]}},[2,4],[3,4],[4,4]},
         genSigns => 1, field => ZZ/5)

o1 = L

o1 : LieAlgebra
i2 : symmCyclePermLie {{0,4}}
the map is not welldefined
i3 : symmCyclePermLie {{0,4},{1,3}}

o3 = MapLie{...7...}

o3 : MapLie
i4 : peek oo

o4 = MapLie{0 => [4]      }
            1 => [3]
            2 => [2]
            3 => [1]
            4 => [0]
            sourceLie => L
            targetLie => L

See also