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OverviewEmanating 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. Full Product DetailsAuthor: David E. HandelmanPublisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K Edition: 1987 ed. Volume: 1282 Dimensions: Width: 15.50cm , Height: 0.80cm , Length: 23.50cm Weight: 0.490kg ISBN: 9783540184003ISBN 10: 3540184007 Pages: 138 Publication Date: 07 October 1987 Audience: College/higher education , Professional and scholarly , Undergraduate , Postgraduate, Research & Scholarly Format: Paperback Publisher's Status: Active Availability: In Print This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsDefinitions 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.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |