Orthogonal decompositions and integral lattices / by Alexei I. Kostrikin, Pham Huu Tiep.

Format:

Book

Author/Creator:

Kostrikin, A. I. (Alekseĭ Ivanovich)

Contributor:

Pham, Huu Tiep, 1963-

Series:

De Gruyter Expositions in Mathematics

De Gruyter expositions in mathematics, 0938-6572 ; 15

De Gruyter Expositions in Mathematics , 0938-6572 ; 15

Language:

English

Subjects (All):

Lie algebras.

Orthogonal decompositions.

Lattice theory.

Physical Description:

1 online resource (548 p.)

Edition:

Reprint 2011

Place of Publication:

Berlin ; New York : Walter de Gruyter, 1994.

Language Note:

English

Summary:

The aim of the Expositions is to present new and important developments in pure and applied mathematics. Well established in the community over more than two decades, the series offers a large library of mathematical works, including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers interested in a thorough study of the subject. Editorial Board Lev Birbrair , Universidade Federal do Cear , Fortaleza, Brasil Walter D. Neumann , Columbia University, New York, USA Markus J. Pflaum , University of Colorado, Boulder, USA Dierk Schleicher , Jacobs University, Bremen, Germany Katrin Wendland , University of Freiburg, Germany Honorary Editor Victor P. Maslov , Russian Academy of Sciences, Moscow, Russia Titles in planning include Yuri A. Bahturin, Identical Relations in Lie Algebras (2019) Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups , Volume 2 (2019) Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019) Volker Mayer, Mariusz Urbański, and Anna Zdunik, Random and Conformal Dynamical Systems (2021) Ioannis Diamantis, Bostjan Gabrovsek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)

Contents:

Frontmatter

Preface

Introduction

Part I Orthogonal decompositions of complex simple Lie algebras

Chapter 1 Type An

Chapter 2 The types Βn, Cn and Dn

Chapter 3 Jordan subgroups and orthogonal decompositions

Chapter 4 Irreducible orthogonal decompositions of Lie algebras with special Coxeter number

Chapter 5 Classification of irreducible orthogonal decompositions of complex simple Lie algebras of type An

Chapter 6 Classification of irreducible orthogonal decompositions of complex simple Lie algebras of type Bn

Chapter 7 Orthogonal decompositions of semisimple associative algebras

Part II Integral lattices and their automorphism groups

Chapter 8 Invariant lattices of type G2 and the finite simple group G2(3)

Chapter 9 Invariant lattices, the Leech lattice and even unimodular analogues of it in Lie algebras of type Ap-1

Chapter 10 Invariant lattices of type Apm-1

Chapter 11 The types B2m-1 and D2m

Chapter 12 Invariant lattices of types F4 and E6, and the finite simple groups L4(3) , Ω7(3) , Fi22

Chapter 13 Invariant lattices of type E8 and the finite simple groups F3, L4(5)

Chapter 14 Other lattice constructions

Appendix

Bibliography

Notation

Author Index

Subject Index

Notes:

Description based upon print version of record.

Includes bibliographical references (p. [511]-525) and indexes.

Description based on online resource; title from PDF title page (publisher's Web site, viewed 08. Jul 2019)

ISBN:

9783110901757

3110901757

OCLC:

979589464