Search results for "indecomposable"
showing 3 items of 13 documents
Surfaces of minimal degree of tame representation type and mutations of Cohen–Macaulay modules
2017
We provide two examples of smooth projective surfaces of tame CM type, by showing that any parameter space of isomorphism classes of indecomposable ACM bundles with fixed rank and determinant on a rational quartic scroll in projective 5-space is either a single point or a projective line. For surfaces of minimal degree and wild CM type, we classify rigid Ulrich bundles as Fibonacci extensions. For the rational normal scrolls S(2,3) and S(3,3), a complete classification of rigid ACM bundles is given in terms of the action of the braid group in three strands.
IRREDUCIBLE COXETER GROUPS
2004
We prove that a non-spherical irreducible Coxeter group is (directly) indecomposable and that an indefinite irreducible Coxeter group is strongly indecomposable in the sense that all its finite index subgroups are (directly) indecomposable. Let W be a Coxeter group. Write W = WX1 × ⋯ × WXb × WZ3, where WX1, … , WXb are non-spherical irreducible Coxeter groups and WZ3 is a finite one. By a classical result, known as the Krull–Remak–Schmidt theorem, the group WZ3 has a decomposition WZ3 = H1 × ⋯ × Hq as a direct product of indecomposable groups, which is unique up to a central automorphism and a permutation of the factors. Now, W = WX1 × ⋯ × WXb × H1 × ⋯ × Hq is a decomposition of W as a dir…
Semi-terminal continua in homogeneous spaces
2016
A semi-terminal continuum Y in a space X is defined by the condition that no two disjoint subcontinua of X intersect both Y and X-Y. Though numerous obvious examples of such continua can be found in arcs, trees and tree-like continua, these examples are related to the non-homogeneity of the space, and having semi-terminal continua in a homogeneous continuum is counter-intuitive. Recently, a large collection of homogeneous spaces with semi-terminal, non-terminal subcontinua has been found. This paper is devoted to studying these spaces and the general structure of homogeneous continua related to the presence of semi-terminal subcontinua.