Given a quantized enveloping algebra U returns the map from U onto the integral form of the universal enveloping algebra of the corresponding Lie algebra (cf. Section The Z-form of Uq(L)). We refer to Section Universal Enveloping Algebras for an account of universal enveloping algebras in Magma.
> U:= QuantizedUEA(RootDatum("C3")); > f:= QUAToIntegralUEAMap(U); > p:= CanonicalElements(U, [1,2,1]); > [ f(u) : u in p ]; [ y_1*y_2^(2)*y_3, 2*y_1*y_2^(2)*y_3 + y_1*y_2*y_5, y_1*y_2^(2)*y_3 + y_1*y_2*y_5 + y_1*y_7, y_1*y_2^(2)*y_3 + y_2*y_3*y_4 - y_2*y_6, 2*y_1*y_2^(2)*y_3 + y_1*y_2*y_5 + y_2*y_3*y_4 - y_2*y_6 + y_4*y_5, 2*y_1*y_2^(2)*y_3 + y_1*y_2*y_5 + 2*y_2*y_3*y_4 - y_2*y_6 + y_4*y_5, y_1*y_2^(2)*y_3 + y_1*y_2*y_5 + y_2*y_3*y_4 + y_1*y_7 + y_4*y_5 + y_8 ]So this allows one to construct elements of the canonical basis of a universal enveloping algebra (of a semisimple Lie algebra). [Next][Prev] [Right] [Left] [Up] [Index] [Root]