Description

Book Synopsis
Studies the interplay between various algebraic, geometric and combinatorial aspects of real hyperplane arrangements. This volume provides a careful, organised and unified treatment of several recent developments in the field, and brings forth many new ideas and results. It has two parts, each divided into eight chapters, and five appendices with background material.

Table of Contents
  • Part I: Hyperplane arrangements
  • Cones
  • Lunes
  • Category of lunes
  • Reflection arrangements
  • Braid arrangement and related examples
  • Descent and lune equations
  • Distance functions and Varchenko matrix
  • Part II: Birkhoff algebra and Tits algebra
  • Lie and Zie elements
  • Eulerian idempotents
  • Diagonalizability and characteristic elements
  • Loewy series and Peirce decompositions
  • Dynkin idempotents
  • Incidence algebras
  • Invariant Birkhoff algebra and invariant Tits algebra
  • Appendices: Regular cell complexes
  • Posets
  • Incidence algebras of posets
  • Algebras and modules
  • Bands
  • References: Bibliography
  • Notation index
  • Subject index.

    Topics in Hyperplane Arrangements

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      A Hardback by Marcelo Aguiar, Swapneel Mahajan

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        Publisher: MP-AMM American Mathematical
        Publication Date: Publication Date: 12/30/2017 12:00:00 AM
        ISBN13: 9781470437114, 978-1470437114
        ISBN10: 1470437112

        Description

        Book Synopsis
        Studies the interplay between various algebraic, geometric and combinatorial aspects of real hyperplane arrangements. This volume provides a careful, organised and unified treatment of several recent developments in the field, and brings forth many new ideas and results. It has two parts, each divided into eight chapters, and five appendices with background material.

        Table of Contents
        • Part I: Hyperplane arrangements
        • Cones
        • Lunes
        • Category of lunes
        • Reflection arrangements
        • Braid arrangement and related examples
        • Descent and lune equations
        • Distance functions and Varchenko matrix
        • Part II: Birkhoff algebra and Tits algebra
        • Lie and Zie elements
        • Eulerian idempotents
        • Diagonalizability and characteristic elements
        • Loewy series and Peirce decompositions
        • Dynkin idempotents
        • Incidence algebras
        • Invariant Birkhoff algebra and invariant Tits algebra
        • Appendices: Regular cell complexes
        • Posets
        • Incidence algebras of posets
        • Algebras and modules
        • Bands
        • References: Bibliography
        • Notation index
        • Subject index.

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