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Quadratic Forms

Combinatorics and Numerical Results

  • Michael Barot
  • Jesús Arturo Jiménez González
  • José-Antonio de la Peña

Part of the Algebra and Applications book series (AA, volume 25)

Table of contents

  1. Front Matter
    Pages i-xx
  2. Michael Barot, Jesús Arturo Jiménez González, José-Antonio de la Peña
    Pages 1-42
  3. Michael Barot, Jesús Arturo Jiménez González, José-Antonio de la Peña
    Pages 43-74
  4. Michael Barot, Jesús Arturo Jiménez González, José-Antonio de la Peña
    Pages 75-99
  5. Michael Barot, Jesús Arturo Jiménez González, José-Antonio de la Peña
    Pages 101-134
  6. Michael Barot, Jesús Arturo Jiménez González, José-Antonio de la Peña
    Pages 135-180
  7. Michael Barot, Jesús Arturo Jiménez González, José-Antonio de la Peña
    Pages 181-211
  8. Back Matter
    Pages 213-220

About this book

Introduction

This monograph presents combinatorial and numerical issues on integral quadratic forms as originally obtained in the context of representation theory of algebras and derived categories.

Some of these beautiful results remain practically unknown to students and scholars, and are scattered in papers written between 1970 and the present day. Besides the many classical results, the book also encompasses a few new results and generalizations.

The material presented will appeal to a wide group of researchers (in representation theory of algebras, Lie theory, number theory and graph theory) and, due to its accessible nature and the many exercises provided, also to undergraduate and graduate students with a solid foundation in linear algebra and some familiarity on graph theory.

Keywords

integral quadratic form signed graph reduction algorithm roots and root systems radicals and their extensions Weyl group Coxeter matrix weak positivity weak nonnegativity Dynkin diagram Euclidean diagram inflation and deflation one-point extension MSC (2010): 11D09, 11D45, 05C50

Authors and affiliations

  • Michael Barot
    • 1
  • Jesús Arturo Jiménez González
    • 2
  • José-Antonio de la Peña
    • 3
  1. 1.Kantonsschule SchaffhausenSwitzerland
  2. 2.Instituto de Matemáticas, UNAMMexico
  3. 3.Instituto de Matemáticas, UNAMMiembro de El Colegio NacionalMexico

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-030-05627-8
  • Copyright Information Springer Nature Switzerland AG 2019
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-030-05626-1
  • Online ISBN 978-3-030-05627-8
  • Series Print ISSN 1572-5553
  • Series Online ISSN 2192-2950
  • Buy this book on publisher's site