Author | Handelman, David E. author |
---|---|

Title | Positive Polynomials, Convex Integral Polytopes, and a Random Walk Problem [electronic resource] / by David E. Handelman |

Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1987 |

Connect to | http://dx.doi.org/10.1007/BFb0078909 |

Descript | XIV, 138 p. online resource |

SUMMARY

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

CONTENT

Definitions and notation -- A random walk problem -- Integral closure and cohen-macauleyness -- Projective RK-modules are free -- States on ideals -- Factoriality and integral simplicity -- Meet-irreducibile ideals in RK -- Isomorphisms

Mathematics
Algebra
Mathematical analysis
Analysis (Mathematics)
Geometry
Mathematics
Analysis
Algebra
Geometry