Mathematical Notes
Here are several short notes, written mainly for my benefit or for the benefit of my students. Each file is in pdf format.
Algebraic Groups, Grassmannians, and Flag Varieties
The Alternating Group
A
n
is simple for
n > 4
Artin's Construction of an Algebraic Closure of a Field
Automorphisms of
S
n
and
A
n
Central Simple Algebras
The Classification of Wallpaper Patterns
Computing the Symmetry Groups of the Platonic Solids with the Help of Maple
Direct Limits
Division Algebras over Local Fields
Dualities in Lattice Theory
Examples of Localization
Group Actions
Group Actions,
p
-Groups, and the Sylow Theorems
Group Extensions and
H
3
Isometries of R
n
Locally Free Sheaves
Nonabelian Cohomology
Normed Vector Spaces and Double Duals
A Note About Profinite Groups
Projective Modules and the Sphere S
2
Rings with no Maximal Ideals
Root Space Decomposition of the Classical Lie Algebras
Semidirect Products
On Severi-Brauer Varieties
Sheaf Cohomology
The Smith Normal Form of a Matrix
Transitive Subgroups of
S
5
Last updated: 05/06/2005