### Polyhedral algebras, arrangements of toric varieties, and their groups, by Winfried Bruns and Joseph Gubeladze

We investigate the automorphism groups of graded algebras defined by
lattice polyhedral complexes and of the corresponding projective
varieties, which form arrangements of projective toric varieties.
It is shown that for wide classes of complexes they are
generated by toric actions, elementary transformations and symmetries
of the underlying complex. The main results extend our previous work
for single polytopes (#203 in this server).

In conjunction with #203 the present paper establishes a polyhedral
generalization of classical K-theoretical objects -- the general linear
group GL_n(k) and its elementary subgroup E_n(k) (k a field). Naturally
there arises a question: is there a further analogy with K-theory that
might lead to a polyhedral K-theory? Already for low dimensional
K-groups this question suggests challenging open problems.

Winfried Bruns <Winfried.Bruns@mathematik.uni-osnabrueck.de>

Joseph Gubeladze <>