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Steinberg Groups for Jordan Pairs 2019 ed. [Hardback]

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  • Formāts: Hardback, 458 pages, height x width: 235x155 mm, weight: 869 g, 2 Illustrations, color; XII, 458 p. 2 illus. in color., 1 Hardback
  • Sērija : Progress in Mathematics 332
  • Izdošanas datums: 11-Jan-2020
  • Izdevniecība: Springer-Verlag New York Inc.
  • ISBN-10: 1071602624
  • ISBN-13: 9781071602621
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Steinberg Groups for Jordan Pairs 2019 ed.Palielināt
  • Formāts: Hardback, 458 pages, height x width: 235x155 mm, weight: 869 g, 2 Illustrations, color; XII, 458 p. 2 illus. in color., 1 Hardback
  • Sērija : Progress in Mathematics 332
  • Izdošanas datums: 11-Jan-2020
  • Izdevniecība: Springer-Verlag New York Inc.
  • ISBN-10: 1071602624
  • ISBN-13: 9781071602621
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9781071602621.html
Keywords:
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, Jordan algebras, 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.
Preface vii
Notation and Conventions xi
Chapter I Groups with commutator relations
1(72)
§1 Nilpotent sets of roots
2(7)
§2 Reflection systems and root systems
9(13)
§3 Groups with commutator relations
22(12)
§4 Categories of groups with commutator relations
34(18)
§5 Weyl elements
52(21)
Chapter II Groups associated with Jordan pairs
73(66)
§6 Introduction to Jordan pairs
74(22)
§7 The projective elementary group I
96(16)
§8 The projective elementary group II
112(11)
§9 Groups over Jordan pairs
123(16)
Chapter III Steinberg groups for Peirce graded Jordan pairs
139(45)
§10 Peirce gradings
139(13)
§11 Groups defined by Peirce gradings
152(8)
§12 Weyl elements for idempotent Peirce gradings
160(8)
§13 Groups defined by sets of idempotents
168(16)
Chapter IV Jordan graphs
184(81)
§14 3-graded root systems
185(19)
§15 Jordan graphs and 3-graded root systems
204(16)
§16 Local structure
220(12)
§17 Classification of arrows and vertices
232(13)
§18 Bases
245(9)
§19 Triangles
254(11)
Chapter V Steinberg groups for root graded Jordan pairs
265(98)
§20 Root gradings
266(6)
§21 Groups defined by root gradings
272(19)
§22 The Steinberg group of a root graded Jordan pair
291(14)
§23 Cogs
305(21)
§24 Weyl elements for idempotent root gradings
326(19)
§25 The monomial group
345(12)
§26 Centrality results
357(6)
Chapter VI Central closedness
363(80)
§27 Statement of the main result and outline of the proof
364(8)
§28 Invariant alternating maps
372(12)
§29 Vanishing of the binary symbols
384(14)
§30 Vanishing of the ternary symbols
398(17)
§31 Definition of the partial sections
415(12)
§32 Proof of the relations
427(16)
Bibliography 443(6)
Subject Index 449(4)
Notation Index 453