#### Wolfgang Globke

Office: 726
Phone: +61 8 8313 6184

School of Mathematical Sciences
Australia

#### –– Preprints ––

• D. Burde, W. Globke, A. Minchenko, Étale representations for reductive algebraic groups with factors Sp(n) or SO(n)

arXiv:1706.08735

#### –– Journal Articles ––

1. W. Globke, Y. Nikolayevsky, Compact pseudo-Riemannian homogeneous Einstein manifolds of low dimension
2. D. Burde, W. Globke, Étale representations for reductive algebraic groups with one-dimensional center

Journal of Algebra 487, 2017, 200-216 (also arXiv:1606.01643)

3. O. Baues, W. Globke, Rigidity of compact pseudo-Riemannian homogeneous spaces for solvable Lie groups

to appear in International Mathematics Research Notices (also arXiv:1507.02575)

4. W. Globke, T. Leistner, Locally homogeneous pp-waves
5. W. Globke, A Supplement to the Classification of Flat Homogeneous Spaces of Signature (m,2)
6. W. Globke, On the Geometry of Flat Pseudo-Riemannian Homogeneous Spaces
7. W. Globke, Holonomy Groups of Complete Flat Pseudo-Riemannian Homogeneous Spaces
8. O. Baues, W. Globke, Flat pseudo-Riemannian homogeneous spaces with non-abelian holonomy group

#### –– Theses ––

• Doctoral Thesis: Holonomy Groups of Flat Pseudo-Riemannian Homogeneous Manifolds (pdf)

Karlsruhe Institute of Technology, 2011

There are MuPAD files available to facilitate computations involving the non-abelian holonomy groups in dimensions 8 (geodesically incomplete) and 14 (geodesically complete) from part II of my thesis.

• Diploma Thesis: Étale Representations of Reductive Algebraic Groups and Left-Symmetric Algebras (pdf)

Universität Karlsruhe (TH), 2007

Addendum: The file Tables of Prehomogeneous Modules (pdf) contains all tables from my diploma thesis.

#### –– Course Notes ––

English translation of the course notes below, but still work in progress. Comments and corrections are very welcome!

• Lineare Algebra II für Informatik (pdf)

Course Notes in German, 2012

#### –– Translations ––

• J. Dorfmeister, M. Koecher, Relative invariants and non-associative algebras (pdf)

This is a translation of Josef Dorfmeister and Max Koecher's long treatise on homogeneous domains and the associated relative invariants and algebras. I took the liberty of changing some of the fonts to be more to my liking, but the letters used to denote the objects in the text remained the same.

• H. Freudenthal, Octaves, Exceptional Groups and Octave Geometry (pdf)

This is a translation of Hans Freudenthal's paper on octonion geometry (or "octaves", as he calls them) published in 1985.

• J. Helmstetter, Left-symmetric algebras (pdf)

This is a translation of Jacques Helmstetter's paper on left-symmetric algebras. The French original is difficult to obtain.

• J. Helmstetter, The radical of a left-symmetric algebra (pdf)

Jacques Helmstetter's second paper on left-symmetric algebras, which is a collection of several fundamental results in this field.

• C. Hermite, On the exponential function (pdf)

Hermite was the first to prove the transcendence of the Euler number in this article. The techniques developed to study the transcendence of numbers are to a large part inspired by Hermite's approach here.

• E. Kähler, On a remarkable Hermitian metric (pdf)

This is a translation of the classical German paper Über eine bemerkenswerte Hermitesche Metrik written in 1932 by Erich Kähler. In this paper he introduced the special class of Riemannian metrics nowadays called Kähler metrics in his honour. Kähler's prose resembles that of a 19th century German academic, meaning it consists mostly of seemingly endless convoluted sentences. In translating I tried to stay as close as possible to his original notation and wording – after all, just because you do not speak German it does not mean you should not have to suffer, does it?

• E. Kähler, The inner differential calculus (pdf)

Another literary masterpiece by Erich Kähler from 1962. This paper develops the inner differential calculus, nowadays unfortunately often named geometric algebra. Kähler's contribution is often overlooked, even though he developed the theory independently of and more rigorously than similar developments at around the same time.

• M. Koecher, The Riccati differential equation and non-associative algebras (pdf)

Max Koecher's curious text relates Riccati differential equations to Jordan algebras.

• D. Luna, On closed orbits of reductive algebraic groups (pdf)

This is a translation of Domingo Luna's paper on closed orbits for reductive groups given the existence of an invariant scalar product, published in 1972.

• D. Luna, Étale slices (pdf)

Luna improves the previous paper and finds a slice theorem for the action of reductive algebraic groups on affine varieties, analogous to the slice theorem for compact Lie groups on differentiable manifolds.

• W. Magnus, On groups and associated Lie rings (pdf)

A paper on Lie rings associated to finite groups. I thought this might be interesting, but now I'm not so sure.

• C.L. Siegel, On Riemann's unpublished works in analytic number theory (pdf)

A translation of Carl Ludwig Siegel's text Über Riemanns Nachlaß zur analytischen Zahlentheorie from 1932. This survey of Riemann's lost papers on his ideas and calculations on the zeta function was a kickstarter for the Riemann hypothesis business.

• G. Wüstholz, Algebraic points in analytic subgroups of algebraic groups (pdf)

Wüstholz's seminal paper in the theory of transcendental numbers. Unfortunately it cites a lot from other papers that are available in German only.

• H. Zassenhaus, Proof of a theorem on discrete groups (pdf)

This is a translation of Hans Zassenhaus's seminal paper on small group elements. It has become very influential in the theory of discrete subgroups of Lie groups. This paper is often mistakenly assigned the year 1938, but the issue was indeed published in 1937. Some typos were fixed and a few additional comments added.

• H. Zassenhaus, On an algorithm to determine the space groups (pdf)

This is a translation of a paper published in 1948 by Hans Zassenhaus. He develops an algorithm to generate all the space groups (crystallographic groups) for a given dimension n. In the translation I slightly changed the original notation for rings and fields by using the modern notation $$\mathbb{Z}$$, $$\mathbb{Q}$$ and $$\mathbb{R}$$ for integer, rational and real numbers, respectively. Some typos were corrected and an index was added.

#### –– Expositions ––

• The Auslander conjecture: Where is Auslander's mistake? (pdf)

An analysis of Louis Auslander's infamous 1964 paper on flat affine manifolds. This paper gave rise to the conjecture that the fundamental group of every compact complete flat affine manifold is virtually polycyclic.

• Kinematik des Puma 200 (pdf)

Mobile Robotics Lab (University of Karlsruhe), 2005

• Oberflächenrekonstruktion aus Punktwolken (pdf)

Seminar on Medical Simulation Systems (University of Karlsruhe), 2005

• Software-Metriken (pdf)

Seminar on Modern Software Development (University of Karlsruhe), 2005

• Algorithmen für Gruppen und Codes (pdf)

Notes on a course given by Markus Grassl (University of Karlsruhe), 2005

• Symbolische Vereinfachung polynomialer Gleichungssysteme (pdf)

Notes on a course given by Rainer Steinwandt (University of Karlsruhe), 2005

• Markovketten und verdeckte Markovmodelle (pdf)

Seminar on Bioinformatics (University of Karlsruhe), 2001