Name: Winfried Bruns
Title: Polyhedral $K_2$
Abstract:
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.
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