Let g be an affine Kac-Moody algebra with symmetric Cartan datum, n be the maximal nilpotent subalgebra of g. By the Hall algebra approach, we construct integral bases of the Z-form of the enveloping algebra U(n). In particular, the representation theory of tame quivers is essentially used in this paper.

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 ...

The aim of this work is to study the ramification of quaternion algebras over the function field of a stable elliptic surface, in particular over the field of complex numbers. Over number fields there are criteria for the ramification of quaternion algebras such as the tame symbol formula. We study how this formula can be interpreted in a geometrical way, and how the ramification relates to the...

For a finite dimensional algebra A over an algebraically closed field, let T (A) denote the trivial extension of A by its minimal injective cogenerator bimodule. We prove that, if TA is a tilting module and B = EndTA, then T (A) is tame if and only if T (B) is tame. Introduction. Let k be an algebraically closed field. In this paper, an algebra A is always assumed to be associative, with an ide...

Let 1c "be a field and A a finite-dimensional 7c-algebra (associative, with 1). AVe consider representations of A as rings of endomorpliisms of finitedimensional 7c-spaces, and thus JL-modules, and we ask for a classification of such representations. More generally, we may consider the following problem: given an abelian category # and simple ( = irreducible) objects F(l),..., B(n) in #, what a...

Abstract Using formal-local methods, we prove that a separated and normal tame Artin surface has the resolution property. By proving stacks can be rigidified, ultimately reduce our analysis to establishing existence of Azumaya algebras. Our construction passes through case gerbes, curves, algebraic space surfaces, each which establish independently.

Let k be an arbitrary field, Λ a k-algebra and V Λ-module. When it exists, the universal deformation ring R(Λ,V) of is whose local homomorphisms to R parametrize lifts up R⊗kΛ, where any complete, commutative Noetherian with residue field k. Symmetric special biserial algebras, which coincide Brauer graph can viewed as generalizing blocks finite type p-modular group algebras. Bleher Wackwitz cl...