|
Mathematisches Institut der Universität München
- B. Pareigis
Prof. Dr. Bodo Pareigis
NMSU Homepage of Bodo Pareigis - the Quantum
Group Page
From the San Diego Union (8/22/99):
As part of the state
prison system's Joint Venture Program, inmates at the Richard J. Donovan
Correctional Facility who are hired for this job will learn to operate
machines, check products for quality control, and ship and receive goods
for The Quantum Group Inc.
|
These lecture notes on
Quantum Groups
will be updated and completed as further sections become available. You
can either read and download full chapters or single sections.
| Table
of Contents: |
update: |
format: |
| Chapter 1: |
Commutative and Noncommutative Algebraic Geometry |
09-20-99 |
 |
 |
 |
|
The Principles of Commutative Algebraic Geometry |
09-17-99 |
|
|
|
|
Quantum Spaces and Noncommutative Geometry |
09-20-99 |
|
|
|
|
Quantum Monoids and their Actions on Quantum Spaces |
09-20-99 |
|
|
|
| Chapter 2: |
Hopf Algebras, Algebraic, Formal, and Quantum Groups |
11-03-99 |
|
|
|
|
Hopf Algebras |
09-20-99 |
|
|
|
|
Monoids and Groups in a Category |
09-29-99 |
|
|
|
|
Affine Algebraic Groups |
11-03-99 |
|
|
|
|
Formal Groups |
11-03-99 |
|
|
|
|
Quantum Groups |
11-03-99 |
|
|
|
|
Quantum Automorphism Groups |
11-03-99 |
|
|
|
|
Duality of Hopf Algebras |
11-03-99 |
|
|
|
| Chapter 3: |
Representation Theory, Reconstruction and Tannaka
Duality |
11-03-99 |
|
|
|
|
Representations of Hopf Algebras |
11-03-99 |
|
|
|
|
Monoidal Categories |
11-03-99 |
|
|
|
|
Dual Objects |
11-03-99 |
|
|
|
|
Finite reconstruction |
11-03-99 |
|
|
|
|
The coalgebra coend |
11-03-99 |
|
|
|
|
The bialgebra coend |
11-03-99 |
|
|
|
|
The quantum monoid of a quantum space |
11-03-99 |
|
|
|
|
Reconstruction and C-categories |
11-03-99 |
|
|
|
| Chapter 4: |
The Infinitesimal Theory |
12-2-99 |
|
|
|
|
Integrals and Fourier Transforms |
12-2-99 |
|
|
|
|
Derivations |
12-2-99 |
|
|
|
|
The Lie Algebra of Primitive Elements |
12-2-99 |
|
|
|
|
Derivations and Lie Algebras of Affine Algebraic Groups |
12-2-99 |
|
|
|
| Chapter 5: |
The Quantum Yang-Baxter Equation, Braided Categories,
and the Drinfel'd Double |
|
 |
|
|
| Apendix: |
Toolbox |
09-17-99 |
|
|
|
|
Categories |
09-17-99 |
|
|
|
|
Functors |
09-17-99 |
|
|
|
|
Natural Transformations |
09-17-99 |
|
|
|
|
Tensor Products |
09-17-99 |
|
|
|
|
Algebras |
09-17-99 |
|
|
|
|
Coalgebras |
09-17-99 |
|
|
|
|
Bialgebras |
09-17-99 |
|
|
|
|
Representable Functors |
09-17-99 |
|
|
|
|
Adjoint Functors and the Yoneda Lemma |
09-17-99 |
|
|
|
|
Limits and Colimits, Products and Equalizers |
11-18-99 |
|
|
|
These lecture notes are readable with a dvi reader as supplied with most
TeX or LaTeX systems. To copy these preprints to your own server you can,
on some systems, click the link with the RIGHT mouse key and choose the
download command.
A DVI previewer can be found in http://www.tex.ac.uk/tex-archive/dviware/dviwin/
in the file dviwin29.zip. After unpacking read the readme file for the
installation. Be sure to install properly all font files, that come for
the TeX system. A shareware program to unzip ZIP files is in http://www.pkware.com/download.html.
The ps-version can be read with a ghostview program. The pdf version can be
read with Adobe Acrobat Reader.
If you visit my Munich
home page. you can find further lecture notes and publications.
Updated 2. Dec. 1999 by B. Pareigis
|
