Higher polyhedral K-groups

Polyhedral K_2

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-dime…

Polytopes and K-theory

This is an overview of 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''. A conjecture is proposed on the structure of higher polyhedral K-groups for certain class of polytopes for which the coincidence of Quillen's and Volodin's theories is known.

环面和旗簇的K-理论的多面体模型

Polyhedral models for K-theory of toric and flag varieties

将Pukhlikov-Khovanskii型表示推广到环面和旗簇的K-理论，通过构造与线性多面体族相关的K-环，并证明其可实现为相应簇的K-理论。