Polytopes, rings and K-theory
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چکیده
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منابع مشابه
2 Winfried Bruns And
We overview results from our experiment of merging two seemingly unrelated disciplines – higher algebraic K-theory of rings and the theory of lattice polytopes. The usual K-theory is the “theory of a unit simplex”. The text is based on the works [BrG1, BrG5, BrG6]. Further related results are found in [BrG2, BrG3, BrG4]. At the end of the paper we propose a general conjecture on the structure o...
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In the first part of the paper we survey some far reaching applications of the basis facts of linear programming to the combinatorial theory of simple polytopes. In the second part we discuss some recent developments concurring the simplex algorithm. We describe sub-exponential randomized pivot roles and upper bounds on the diameter of graphs of polytopes.
متن کاملar X iv : m at h / 01 08 01 3 v 1 [ m at h . K T ] 2 A ug 2 00 1 HIGHER POLYHEDRAL K - GROUPS
We define higher polyhedral K-groups for commutative rings, starting from the stable groups of elementary automorphisms of polyhedral algebras. Both Volodin’s theory and Quillen’s + construction are developed. In the special case of algebras associated with unit simplices one recovers the usual algebraic K-groups, while the general case of lattice polytopes reveals many new aspects, governed by...
متن کاملBruns And
We define higher polyhedral K-groups for commutative rings, starting from the stable groups of elementary automorphisms of polyhedral algebras. Both Volodin’s theory and Quillen’s + construction are developed. In the special case of algebras associated with unit simplices one recovers the usual algebraic K-groups, while the general case of lattice polytopes reveals many new aspects, governed by...
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Unprojection theory analyzes and constructs complicated commutative rings in terms of simpler ones. Our main result is that, on the algebraic level of Stanley-Reisner rings, stellar subdivisions of Gorenstein* simplicial complexes correspond to unprojections of type Kustin-Miller. As an application of our methods we study the minimal resolution of Stanley– Reisner rings associated to stacked po...
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تاریخ انتشار 2007