Overview
- Develops a unified theory of Steinberg groups, independent of matrix representations, based on the theory of Jordan pairs and the theory of 3-graded locally finite root systems
- Simplifies the case-by-case arguments and explicit matrix calculations made in much of the existing literature
- Offers new approaches and original concepts to add clarity to the study of Steinberg groups
Part of the book series: Progress in Mathematics (PM, volume 332)
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About this book
The development of this approach occurs over six chapters, progressing from groups with commutator relations and their Steinberg groups, then on to Jordan pairs, 3-graded locally finite root systems, and groups associated with Jordan pairs graded by root systems, before exploring the volume's main focus: the definition of the Steinberg group of a root graded Jordan pair by a small set of relations, and its central closedness. Several original concepts, such as the notions of Jordan graphs and Weyl elements, provide readers with the necessary tools from combinatorics and group theory.
Steinberg Groups for Jordan Pairs is ideal for PhD students and researchers in the fields of elementary groups, Steinberg groups, Jordanalgebras, and Jordan pairs. By adopting a unified approach, anybody interested in this area who seeks an alternative to case-by-case arguments and explicit matrix calculations will find this book essential.
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Table of contents (6 chapters)
Authors and Affiliations
Bibliographic Information
Book Title: Steinberg Groups for Jordan Pairs
Authors: Ottmar Loos, Erhard Neher
Series Title: Progress in Mathematics
DOI: https://doi.org/10.1007/978-1-0716-0264-5
Publisher: Birkhäuser New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media, LLC, part of Springer Nature 2019
Hardcover ISBN: 978-1-0716-0262-1Published: 11 January 2020
eBook ISBN: 978-1-0716-0264-5Published: 10 January 2020
Series ISSN: 0743-1643
Series E-ISSN: 2296-505X
Edition Number: 1
Number of Pages: XII, 458
Number of Illustrations: 2 illustrations in colour
Topics: Non-associative Rings and Algebras, K-Theory, Number Theory, Group Theory and Generalizations