A Home Page for Physics 500-006, Fall, 2005
A Seminar in Group Theory, with extra advanced topics
| Fall 2005
| Daniel Finley
|
|
Wednesday, 11:00 - 12:00 Noon, in Room 190 |
This is an experimental seminar, designed to push forward the mathematical techniques
available to the participants.
A somewhat modified version of the syllabus that was put forward last spring is
attached
here.
As we meet only once a week, and as there is more content available than could be covered
in several years, a very important function of this webpage will be to try to list sources
where material may be found in greater depth. At this link is a
beginning list of books that seem suitable
to me, with some notes may be found
Some handouts are also available, listed below:
- Lie Groups:
Some useful definitions and notes (2 pages).
- Lie Algebras:
Some useful definitions and notes (4 pages).
- Root Systems for Simple Lie Algebras:
Works through a description of the properties of all simple, finite-dimensional Lie algebras,
with good descriptions of their basic properties (21 pages).
- Simple Lie Algebras: More details for
algebras of Ranks 1 and 2; Lists of All Ranks (16 pages).
- General Contragredient Algebras:
some very brief notes on more general, infinite-dimensional algebras, but of finite growth
(8 pages).
- Brief Introduction to the use of Weights to
Label (Irreducible) Representations; no examples are given, but, hopefully will be
provided by speakers.
- not too rigorous a definition of a manifold,
and the sphere as a simple example.
- Building on the definition/discussion of a manifold just above, I now add two and
a half more files:
- Tangent and co-Tangent Bundles over a
manifold;
- some discussion of Tensor Bundles and especially
what is necessary to study metrics in the tangent bundle, and then to
create arbitrary connections between individual tensor spaces
over points on the manifold, and then to study the curvature of these connections
and its relation to the metric there.
- Lastly, a few notes that are probably not of too much use to this group, mostly about
conventions
for presentations of various sorts of geometric objects that are important here.
- More will come along, I believe.
Some suggested problems: working them out might be useful to get a real feel for the
material. They are not particularly lengthy, although I would use a computer algebra
package, such as Maple, to do them:
- Two Lie algebra calculations.
- A thought about weights.
Last updated/modified: 21 August, 2005
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