Loos / Neher Steinberg Groups for Jordan Pairs

1. Auflage 2020
ISBN: 978-1-0716-0264-5
Verlag: Springer US
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 332, 458 Seiten, eBook

Reihe: Progress in Mathematics

The present monograph 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. 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.

Zielgruppe

Research

Autoren/Hrsg.

Loos, Ottmar

Neher, Erhard

Inhaltsverzeichnis

Preface.- Notation and Conventions.- Groups with Commutator Relations.- Groups Associated with Jordan Pairs.- Steinberg Groups for Peirce Graded Jordan Pairs.- Jordan Graphs.- Steinberg Groups for Root Graded Jordan Pairs.- Central Closedness.- Bibliography.- Subject Index.- Notation Index.