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GradedLieAlgebras :: symmPermLie

symmPermLie -- checks if a permutation of the generators is an automorphism

Synopsis

Description

Input is a permutation of the generators given as a reordered list of the generators. Output is either an error message or the automorphism. The Lie algebra in the example below is the holonomy Lie algebra of the "quadrangle", the graphical arrangement for the complete graph on four vertices.

i1 : L=holonomyLie{{0,1,2},{0,3,4},{1,3,5},{2,4,5}}

o1 = L

o1 : LieAlgebra
i2 : symmPermLie {5,2,4,1,3,0}

o2 = MapLie{...8...}

o2 : MapLie
i3 : peek oo

o3 = MapLie{0 => [5]      }
            1 => [2]
            2 => [4]
            3 => [1]
            4 => [3]
            5 => [0]
            sourceLie => L
            targetLie => L
i4 : f=symmCyclePermLie {{0,5},{1,2,4,3}}

o4 = f

o4 : MapLie
i5 : peek f

o5 = MapLie{0 => [5]      }
            1 => [2]
            2 => [4]
            3 => [1]
            4 => [3]
            5 => [0]
            sourceLie => L
            targetLie => L

See also