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Steinberg groups for Jordan pairs

Author: Ottmar Loos; Erhard Neher
Publisher: New York, NY : Birkhäuser, 2020.
Series: Progress in mathematics (Boston, Mass.), v. 332.
Edition/Format:   eBook : Document : EnglishView all editions and formats
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Loos, Ottmar
Steinberg Groups for Jordan Pairs
New York, NY : Springer Basel AG,c2020
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Ottmar Loos; Erhard Neher
ISBN: 9781071602645 1071602640
OCLC Number: 1136962949
Notes: Description based upon print version of record.
Description: 1 online resource (470 p.).
Contents: Intro --
Contents --
Preface --
Notation and Conventions --
CHAPTER I: GROUPS WITH COMMUTATOR RELATIONS --
1. Nilpotent sets of roots --
2. Reflection systems and root systems --
3. Groups with commutator relations --
4. Categories of groups with commutator relations --
5. Weyl elements --
CHAPTER II: GROUPS ASSOCIATED WITH JORDAN PAIRS --
6. Introduction to Jordan pairs --
7. The projective elementary group I --
8. The projective elementary group II --
9. Groups over Jordan pairs --
CHAPTER III: STEINBERG GROUPS FOR PEIRCE GRADED JORDAN PAIRS --
10. Peirce gradings 11. Groups defined by Peirce gradings --
12. Weyl elements for idempotent Peirce gradings --
13. Groups defined by sets of idempotents --
CHAPTER IV: JORDAN GRAPHS --
14. 3-graded root systems --
15. Jordan graphs and 3-graded root systems --
16. Local structure --
17. Classification of arrows and vertices --
18. Bases --
19. Triangles --
CHAPTER V: STEINBERG GROUPS FOR ROOT GRADED JORDAN PAIRS --
20. Root gradings --
21. Groups defined by root gradings --
22. The Steinberg group of a root graded Jordan pair --
23. Cogs --
24. Weyl elements for idempotent root gradings 25. The monomial group --
26. Centrality results --
CHAPTER VI: CENTRAL CLOSEDNESS --
27. Statement of the main result and outline of the proof --
28. Invariant alternating maps --
29. Vanishing of the binary symbols --
30. Vanishing of the ternary symbols --
31. Definition of the partial sections --
32. Proof of the relations --
Bibliography --
Subject Index --
Notation Index
Series Title: Progress in mathematics (Boston, Mass.), v. 332.
Responsibility: Ottmar Loos, Erhard Neher.

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