Just as a follow-up on how far I got. Suppose I have a Lie algebra with a one-dimensional center. Then I can find that Dimension(Cocycles(lie, 0)) = 1, Dimension(Coboundaries(lie, 0)) = 0, and then I can take this a step further:
z:=Cocycles(lie, 0); b:=Coboundaries(lie, 0); gap> Basis(z/b); Basis( <vector space of dimension 1 over Rationals>, [ <0-cochain> ] ) gap> List(Basis(z/b)); [ <0-cochain> ] gap> List(Basis(z/b))[1]; <0-cochain> But now I have no idea how to work with this 0-cochain. I found a function named CocycleInfo, but cannot seem to figure it out. Any ideas? On Mon, Aug 2, 2021 at 9:51 AM Alan Hylton <agh...@lehigh.edu> wrote: > Howdy, > > For low-dimensional Lie algebras I find myself asking GAP if they have any > cohomology using the calls I learned on this forum: > Dimension(Cocycles(my_lie_algebra, n)) - > Dimension(Coboundaries(my_lie_algebra, n)). Then to get a representative of > any non-trivial cohomology class I wind up doing all the calculations by > hand. > > I'd like to move into higher dimensions, but I cannot quite figure out how > to compute cohomology in GAP. Referencing the page > https://www.gap-system.org/Manuals/doc/ref/chap64.html, I have not seen > any mention of computing cocycles mod coboundaries. Can anyone point me in > the right direction? > > I also find that I do not understand some of the data types; is there a > way to view the internal representation of a cochain? > > Many thanks! > Alan > _______________________________________________ Forum mailing list Forum@gap-system.org https://mail.gap-system.org/mailman/listinfo/forum
