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GradedLieAlgebras :: lieAlgebra

lieAlgebra -- constructing a Lie algebra from its presentation

Synopsis

Description

A generator may be of class Symbol, IndexedVariable or Integer, a relation or a value for the differential should be a generalExpressionLie, see How to write Lie elements.

i1 : L1 = lieAlgebra({a,b}, {{{1,-1},{[a,a,b],[b,b,a]}},[a,a,a,a,b]})

o1 = L1

o1 : LieAlgebra
i2 : computeLie 6

o2 = {2, 1, 1, 1, 1, 0}

o2 : List
i3 : peek L1

o3 = LieAlgebra{cache => CacheTable{...9...}                                   }
                compdeg => 6
                deglength => 2
                field => QQ
                genDiffs => {[], []}
                genSigns => {0, 0}
                gensLie => {a, b}
                genWeights => {{1, 0}, {1, 0}}
                numGen => 2
                relsLie => {{{1, -1}, {[a, a, b], [b, b, a]}}, [a, a, a, a, b]}
i4 : L2=lieAlgebra({a,b,c},{[a,b],[a,c]},genWeights=>{{1,0},{1,0},{2,1}},
                    genSigns=>{1,1,1},
                    genDiffs=>{[],[],{{1,1},{[a,a],[b,b]}}})

o4 = L2

o4 : LieAlgebra
i5 : peek L2

o5 = LieAlgebra{cache => CacheTable{...9...}                    }
                compdeg => 3
                deglength => 2
                field => QQ
                genDiffs => {[], [], {{1, 1}, {[a, a], [b, b]}}}
                genSigns => {1, 1, 1}
                gensLie => {a, b, c}
                genWeights => {{1, 0}, {1, 0}, {2, 1}}
                numGen => 3
                relsLie => {[a, b], [a, c]}
i6 : computeLie 5

o6 = {2, 3, 1, 2, 2}

o6 : List

See also

Ways to use lieAlgebra :