Hey Dima, >> some pedestrian-level representation theory of associative algebras > > > > Do you mean stuff like representations of path algebras (which are > > highly non-commutative associative algebras)? Minimal projective > > resolutions of basic algebras? I'm currently working on that. > > no, I meant finite-dimensional associative algebras, say defined > by matrix generators or structure constants. (I mostly care for char=0 > case here). > E.g. Magma can compute their absolutely irreducibe representations, > at least for certain fields like number fields. >
Is there a reference for how to construct these irreps? We have finite-dimensional matrix algebras whose multiplication is given by matrices. I have code for finite-dimensional Lie algebras given by structure coefficients that could easily be expanded to cover algebras (and infinite dimensional). Hey Nathann, - We currently do not have native support for Lie algebras and quantum groups (although these can be accessed through GAP), but I'm working on this. (Although we do have some support for representations of Kac-Moody Lie algebras (over CC) through crystals.) IDK if other M's have support for these, but I think could support better: - General CW or cubical complexes. Our simplicial complexes are okay, but could likely be improved as well. Actually, I don't think there's much code for algebraic topology... - There are no infinite chain complexes implemented in Sage (with this we could potentially help the previous point). - Knot theory (but is being worked on). - Probability theory, on finite sets in particular, or at least having things phrased like how I learned it in classes (like random variables, distributions, etc.) Best, Travis -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
