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.
The paper is here:
The paper is here: http://xxx.uni-augsburg.de/abs/math.KT/0104206.