On Feb 17, 7:57 am, javier <vengor...@gmail.com> wrote: > Hi all, > > I am trying to use sage to compute the Artin-Wedderburn decomposition > of a group algebra.
I am curious to know, how you are doing this. IMHO for this you need to know each irreducible representation explicitly --- but then you can just stack up the right number of copies of each irreducible. Or you rather mean a weaker decomposition, into direct sums of "homogeneous components", where the latter are isomorphic to direct sums of copies of the same irreducible? Dima Since I need exact expressions I am working over > QQbar rather than over CC. When trying to compute the idempotents I > get an error resulting from an attempt to coerce a rational number > into QQbar. A minimal exaple follows: > > sage: G = SymmetricGroup(3) > sage: K = QQbar > sage: A = GroupAlgebra(G,K) > sage: characters = G.irreducible_characters() > sage: idims = [1/x(G(1)) for x in characters] > sage: K(idims[0]) > Traceback (most recent call last): > ... > TypeError: Illegal initializer for algebraic number > > Observe that in this situation the numbers I am trying to coerce into > K are rational: > > sage: idims > [1, 1/2, 1] > > Is this a bug or a feature of QQbar? > > Cheers > J -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
