Search results for "Indecomposable"
showing 10 items of 13 documents
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…
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.
The terminal hyperspace of homogeneous continua
2010
Abstract We investigate the structure of the collection of terminal subcontinua in homogeneous continua. The main result is a reduction of this structure to six specific types. Three of these types are of one-dimensional spaces, and examples representing these types are known. It is not known whether higher dimensional examples having non-trivial terminal subcontinua and representing the three remaining types exist.
Characters, bilinear forms and solvable groups
2016
Abstract We prove a number of results about the ordinary and Brauer characters of finite solvable groups in characteristic 2, by defining and using the concept of the extended nucleus of a real irreducible character. In particular we show that the Isaacs canonical lift of a real irreducible Brauer character has Frobenius–Schur indicator +1. We also show that the principal indecomposable module corresponding to a real irreducible Brauer character affords a quadratic geometry if and only if each extended nucleus is a split extension of a nucleus.
Indecomposable modules over the Virasoro Lie algebra and a conjecture of V. Kac
1991
We consider a class of indecomposable modules over the Virasoro Lie algebra that we call bounded admissible modules. We get results concerning the center and the dimensions of the weight spaces. We prove that these modules always contain a submodule with one-dimensional weight spaces. From this follows the proof of a conjecture of V. Kac concerning the classification of simple admissible modules.
Filament sets and homogeneous continua
2007
Abstract New tools are introduced for the study of homogeneous continua. The subcontinua of a given continuum are classified into three types: filament , non-filament , and ample , with ample being a subcategory of non-filament. The richness of the collection of ample subcontinua of a homogeneous continuum reflects where the space lies in the gradation from being locally connected at one extreme to indecomposable at another. Applications are given to the general theory of homogeneous continua and their hyperspaces.
Indecomposable sets of finite perimeter in doubling metric measure spaces
2020
We study a measure-theoretic notion of connectedness for sets of finite perimeter in the setting of doubling metric measure spaces supporting a weak $(1,1)$-Poincar\'{e} inequality. The two main results we obtain are a decomposition theorem into indecomposable sets and a characterisation of extreme points in the space of BV functions. In both cases, the proof we propose requires an additional assumption on the space, which is called isotropicity and concerns the Hausdorff-type representation of the perimeter measure.
Examples of improjective operators
2000
It has been an open question for some time whether improjective operators are always inessential. Here we give some examples that answer in the negative this question as well as some other related ones, posed in [2, 3, 11, 12]. The description of the examples uses a indecomposable space, constructed by Gowers and Maurey [5], and a characterization of the indecomposable Banach spaces in terms of improjective operators.
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.
A computational criterion for the Kac conjecture
2006
Abstract We give a criterion for the Kac conjecture asserting that the free term of the polynomial counting the absolutely indecomposable representations of a quiver over a finite field of given dimension coincides with the corresponding root multiplicity of the associated Kac–Moody algebra. Our criterion suits very well for computer tests.