#12630: Add representations of quivers and quiver algebras to sage
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Reporter: JStarx | Owner: AlexGhitza
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-5.11
Component: algebra | Resolution:
Keywords: algebra, quiver, module, days49 | Work issues: Split into
different modules. Use parents and elements.
Report Upstream: N/A | Reviewers:
Authors: Jim Stark, Simon King | Merged in:
Dependencies: #12412, #12413 | Stopgaps:
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Comment (by saliola):
Replying to [comment:52 SimonKing]:
> Some comments from a discussion with Nicolas:
>
> - Currently, we say `FreeSmallCategory`. Isn't it simply a semi-group?
If you add the zero element to your set of paths.
> - If it is a semi-group (in particular, if it is declared in the
category of semi-groups, and not in the category of magmas, it might be
possible that we can inherit most of the functionality that is now in
`QuiverAlgebra`. Namely, there already is `Semigroups.Algebras`.
> - Slight problem: Currently, the invalid path is not mentioned in the
list of elements of the free small category / semi-group of a quiver, but
it is ''recognised'' as an element. This is odd, but on the other hand,
when we add it to the list of elements, then the dimension of the algebra
will be one more.
In this case, one wants the "contracted" semigroup algebra (where the 0 of
the algebra is identified with the zero of the semigroup).
PS. I don't have the time right now to follow everything that you are
doing, but I am really interested in this and hope to have a closer look
sometime soon.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12630#comment:57>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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