000 02948nam a22005055i 4500
001 978-3-540-47951-2
003 DE-He213
005 20160624101828.0
007 cr nn 008mamaa
008 121227s1987 gw | s |||| 0|eng d
020 _a9783540479512
_9978-3-540-47951-2
024 7 _a10.1007/BFb0078909
_2doi
050 4 _aQA299.6-433
072 7 _aPBK
_2bicssc
072 7 _aMAT034000
_2bisacsh
082 0 4 _a515
_223
100 1 _aHandelman, David E.
_eauthor.
245 1 0 _aPositive Polynomials, Convex Integral Polytopes, and a Random Walk Problem
_h[electronic resource] /
_cby David E. Handelman.
260 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c1987.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c1987.
300 _aXIV, 138 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1282
505 0 _aDefinitions 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.
520 _aEmanating 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.
650 0 _aMathematics.
650 0 _aAlgebra.
650 0 _aGlobal analysis (Mathematics).
650 0 _aGeometry.
650 1 4 _aMathematics.
650 2 4 _aAnalysis.
650 2 4 _aAlgebra.
650 2 4 _aGeometry.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783540184003
786 _dSpringer
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1282
856 4 0 _uhttp://dx.doi.org/10.1007/BFb0078909
942 _2EBK1648
_cEBK
999 _c30942
_d30942