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Positive Polynomials, Convex Integral Polytopes, and a Random Walk Problem

  • Book
  • © 1987

Overview

Authors:
  1. David E. Handelman
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1282)

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Table of contents (9 chapters)

  1. Front Matter

    Pages I-XI
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  2. Introduction

    • David E. Handelman
    Pages 1-5

  3. Definitions and notation

    • David E. Handelman
    Pages 6-13

  4. A random walk problem

    • David E. Handelman
    Pages 14-27

  5. Integral closure and cohen-macauleyness

    • David E. Handelman
    Pages 28-40

  6. Projective RK-modules are free

    • David E. Handelman
    Pages 41-43

  7. States on ideals

    • David E. Handelman
    Pages 44-49

  8. Factoriality and integral simplicity

    • David E. Handelman
    Pages 50-59

  9. Meet-irreducibile ideals in RK

    • David E. Handelman
    Pages 60-66

  10. Isomorphisms

    • David E. Handelman
    Pages 67-88

  11. Back Matter

    Pages 89-136
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Keywords

About this book

Emanating from the theory of C*-algebras and actions of tori theoren, the problems discussed here are outgrowths of random walk problems on lattices. An AGL (d,Z)-invariant (which is a partially ordered commutative algebra) is obtained for lattice polytopes (compact convex polytopes in Euclidean space whose vertices lie in Zd), and certain algebraic properties of the algebra are related to geometric properties of the polytope. There are also strong connections with convex analysis, Choquet theory, and reflection groups. This book serves as both an introduction to and a research monograph on the many interconnections between these topics, that arise out of questions of the following type: Let f be a (Laurent) polynomial in several real variables, and let P be a (Laurent) polynomial with only positive coefficients; decide under what circumstances there exists an integer n such that Pnf itself also has only positive coefficients. It is intended to reach and be of interest to a general mathematical audience as well as specialists in the areas mentioned.

Bibliographic Information

  • Book Title: Positive Polynomials, Convex Integral Polytopes, and a Random Walk Problem

  • Authors: David E. Handelman

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0078909

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1987

  • Softcover ISBN: 978-3-540-18400-3Published: 07 October 1987

  • eBook ISBN: 978-3-540-47951-2Published: 15 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XIV, 138

  • Topics: Analysis, Algebra, Geometry

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