Computation with Linear Algebraic Groups

2. Auflage 2026
ISBN: 978-1-032-69212-8
Verlag: Taylor & Francis Ltd

Buch, Englisch, 408 Seiten, Format (B × H): 156 mm x 234 mm

Reihe: Chapman & Hall/CRC Monographs and Research Notes in Mathematics

Designed as a self-contained account of a number of key algorithmic problems and their solutions for linear algebraic groups, this book combines in one single text both an introduction to the basic theory of linear algebraic groups and a substantial collection of useful algorithms.

Computation with Linear Algebraic Groups offers an invaluable guide to graduate students and researchers working in algebraic groups, computational algebraic geometry, and computational group theory, as well as those looking for a concise introduction to the theory of linear algebraic groups.

New to the Second Edition:

· Extensive treatment of nilpotent orbits in semisimple Lie algebras

· Includes a new chapter on the orbits in Vinberg representations

· A treatment of Cartan subgroups and their algorithmic applications

Zielgruppe

Academic and Postgraduate

Autoren/Hrsg.

de Graaf, Willem A.

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Zahlentheorie
• Mathematik | Informatik Mathematik Mathematik Allgemein Zahlensysteme

Inhaltsverzeichnis

1. Closed Sets in Affine Space 2. Lie Algebras 3. Linear Algebraic Groups: Basic Constructions 4. Algebraic Groups and Their Lie Algebras 5. Semisimple Algebraic Groups 6. Generators of Arithmetic Groups 7. Invariants of Algebraic Groups 8. Nilpotent Orbits 9. Orbits in Vinberg Representations

Über Autor(innen)

Willem de Graaf obtained his Ph.D. in mathematics from the Eindhoven University of Technology in 1997. Subsequently he earned post-doctoral positions in St Andrews, Utrecht and Linz. From 2005 he held a position in the University of Trento, first as assistant professor and from 2023 as full professor. Apart from numerous research papers on computation with Lie algebras and algebraic groups he wrote large parts of the functionality for Lie Theory of the computer algebra systems GAP4 and Magma.