Universität Leipzig
Fakultät für Mathematik und Informatik
Mathematisches Institut
Wissenschaftlicher Assistent

PD Dr. Axel Schüler

Teaching

PDE for Physicists , lecture course, summer 2007
Linear Algebra for Physicists , lecture course fall/winter 2006/7

Calculus 1 to 4

Information to the Lecture Course Calculus

Analysis 1,2 für Physiker Lecture Prof. Dr. Schmüdgen

Research

My reseach interests are in mathematical physics and algebra. In particular, I am interested in quantum groups and differential calculus on quantum groups and quantum spaces. Quantum groups generalize the concept of Lie groups and universal enveloping algebras of Lie algebras. The first interesting examples of quantum groups were  developed by Drinfeld, Jimbo, Manin, and Woronowicz in the mid 1980s. The quantum group SLq(2) is a deformation of the (commutative) ring of regular functions on the group SL(2). The group structure is reflected in the Hopf algebra structure of  SLq(2). Nowadays, almost all simple Lie groups have one ore more quantum analogues.  Quantum spaces generalize the concept of homogeneous spaces.
It is commonly expected  that quantum groups will provide new ideas  and technics to solve fundamental problems in mathematical physics as the connection of quantum theory and gravitation and the quantum structure of space time  at the Planck scale.
 

Curriculum Vitae

List of Publications

Publications

Notes on the classification of Hopf algebras of dimension pq, in: Hopf algebras, 241--251, Lecture Notes in Pure and Appl. Math., 237, Dekker, New York (2004), abs

Two exterior algebras for orthogonal and symplectic Quantum Groups, Comp. Math. 126 (2001), 57-77, abs

On FRT-Clifford Algebras (with Istvan Heckenberger), Adv. Appl. Clifford Algebras 10 (2001), 267-296, abs

De Rham Cohomology and Hodge decomposition for Quantum Groups (with Istvan Heckenberger), Proc. London Math. Soc. 83 (2001), 743-768, abs

Symmetrizer and Antisymmetrizer of the Birman-Wenzl-Murakami Algebras (with Istvan Heckenberger), Lett. Math Phys. 50 (1999), 45-51, abs

Differential Hopf Algebras on Quantum Groups of Type A , J. Algebra 214 (1999), 479-518, abs

Exterior Algebras Related to the Quantum Group O_q(3)$  (with Istvan Heckenberger), Czech. J. Phys. 48 (1998), 1355-1362, abs

Higher Order Differential Calculus on $SL_q(N)$  (with Istvan Heckenberger), Czech J. Phys. 47 (1997), 1153-1160, abs

Left-covariant differential calculi on SL_q(N)  (with Konrad Schmüdgen),  Banach Cent. Publ. 40 (1997), 185-191 (abs , ps ,dvi , tex )

Left-Covariant Differential Calculi on SL_q(2) and SL_q(3) (with Konrad Schmüdgen), J. Geom. Phys. 20  (1996), 87-105, abs

The Brauer algebra and the Birman-Wenzl-Murakami algebra, Seminar Sophus Lie 3 (1993), 3-11, (abs, ps, dvi)

Covariant bimodules and and differential calculi on quantum groups of type B, C, D, Seminar Sophus Lie 2 (1992), 115-121, (abs, ps, dvi)

Habilitation Theses

Abstract to the Theses ( ps)

Habilitationsschrift (in German) ( ps, tar.gz )

Über die Zerlegung von natürlichen Zahlen in Quadrate (Lecture Test) ( ps, tex )

Colleagues from Leipzig with similar research interests

 Dr. Istvan Heckenberger
 Stefan Kolb
 Ulrich Kraehmer
 Dr. Rainer Matthes
 Prof. Dr. Konrad Schmüdgen
 Elmar Wagner
 Dr. Martin Welk