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GradedLieAlgebras :: lieAlgebra(..., genDiffs => ...)

lieAlgebra(..., genDiffs => ...) -- optional argument for lieAlgebra

Synopsis

Description

This is an option to tell lieAlgebra to assign differential values to the generators. These values should be general Lie expressions, generalExpressionLie, of homological degree one less than the homological degree of the generator and all other weights equal and its sign opposite to the sign of the generator.

i1 : L=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]}}})

o1 = L

o1 : LieAlgebra
i2 : peek L

o2 = 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]}

Observe that L.compdeg = 3, hence computeLie 3 has been executed for L. This is because the program checks that the differential is well-defined and has square zero.

Further information