#16659: Decomposition of finite dimensional associative algebras
-------------------------------------+-------------------------------------
Reporter: virmaux | Owner:
Type: enhancement | Status: new
Priority: major | Milestone: sage-6.4
Component: algebra | Resolution:
Keywords: representation | Merged in:
theory | Reviewers:
Authors: | Work issues:
Report Upstream: N/A | Commit:
Branch: u/virmaux/t/16659 | 434765db324c0e6da9ddab9dd4b02632d12703f9
Dependencies: #11111 | Stopgaps:
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Comment (by saliola):
== semisimple_algebras.py ==
- The `orthogonal_idempotents` method returns **central** orthogonal
idempotents, so I think that the name of this method should be changed
to
`central_orthogonal_idempotents`. For example, in the docstring the
example
`SymmetricGroup(3).algebra(QQ)` returns 3 idempotents, but I expected 4.
- Also, this example doesn't work:
{{{
sage: A3 = SymmetricGroup(3).algebra(QQ)
sage: A3
Symmetric group algebra of order 3 over Rational Field
sage: A3.orthogonal_idempotents()
---------------------------------------------------------------------------
AttributeError Traceback (most recent call
last)
...
AttributeError: 'list' object has no attribute 'map'
}}}
- semisimple vs. semi-simple (be consistent)
- in the following, change the names `listGen`, `topLevel` to be
consistent
with Sage coding conventions:
{{{
+ def _orthogonal_decomposition(self, listGen=None,
topLevel=True):
}}}
- clean up the documentation of `_orthogonal_decomposition`: the last line
("Return a list...") should be the first line
- `orthogonal_idempotents`: what is the definition of a "minimal"
idempotent?
- should there be a `test_orthogonal_idempotents` method?
at the very least, there should be tests to test that the created
idempotents
are indeed orthogonal, sum to the identity, minimal, ....
--
Ticket URL: <http://trac.sagemath.org/ticket/16659#comment:29>
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