Polyhedral K2
نویسنده
چکیده
Using elementary graded automorphisms of polytopal algebras (essentially the coordinate rings of projective toric varieties) polyhedral versions of the group of elementary matrices and the Steinberg and Milnor groups are defined. They coincide with the usual K-theoretic groups in the special case when the polytope is a unit simplex and can be thought of as compact/polytopal substitutes for the tame automorphism groups of polynomial algebras. Relative to the classical case, many new aspects have to be taken into account. We describe these groups explicitly when the underlying polytope is 2-dimensional. Already this low-dimensional case provides interesting classes of groups.
منابع مشابه
Lipschitzian Mappings and Total Mean Curvature
For a smooth closed surface C in E3 the classical total mean curvature is defined by M(C) = ¿/(«i + k2) do(p), where kx, k2 are the principal curvatures at p on C. If C is a polyhedral surface, there is a well known discrete version given by M(C) = IE/,(w a,), where 1¡ represents edge length and a, the corresponding dihedral angle along the edge. In this article formulas involving differentials...
متن کاملThe Steinberg Group of a Monoid Ring, Nilpotence, and Algorithms
For a regular ring R and an affine monoid M the homotheties of M act nilpotently on the Milnor unstable groups of R[M ]. This strengthens the K2 part of the main result of [G5] in two ways: the coefficient field of characteristic 0 is extended to any regular ring and the stableK2-group is substituted by the unstable ones. The proof is based on a polyhedral/combinatorial techniques, computations...
متن کاملLight classes of generalized stars in polyhedral maps on surfaces
A generalized s-star, s ≥ 1, is a tree with a root Z of degree s; all other vertices have degree ≤ 2. Si denotes a generalized 3-star, all three maximal paths starting in Z have exactly i + 1 vertices (including Z). Let M be a surface of Euler characteristic χ(M) ≤ 0, and m(M) := b 5+ √ 49−24χ(M) 2 c. We prove: (1) Let k ≥ 1, d ≥ m(M) be integers. Each polyhedral map G on M with a k-path (on k ...
متن کاملSimple Homotopy Types of Hom-complexes, Neighborhood Complexes, Lovász Complexes, and Atom Crosscut Complexes
In this paper we provide concrete combinatorial formal deformation algorithms, namely sequences of elementary collapses and expansions, which relate various previously extensively studied families of combinatorially defined polyhedral complexes. To start with, we give a sequence of elementary collapses leading from the barycentric subdivision of the neighborhood complex to the Lovász complex of...
متن کاملRobust portfolio selection with polyhedral ambiguous inputs
Ambiguity in the inputs of the models is typical especially in portfolio selection problem where the true distribution of random variables is usually unknown. Here we use robust optimization approach to address the ambiguity in conditional-value-at-risk minimization model. We obtain explicit models of the robust conditional-value-at-risk minimization for polyhedral and correlated polyhedral am...
متن کامل