940 research outputs found
Cluster structures for 2-Calabi-Yau categories and unipotent groups
We investigate cluster tilting objects (and subcategories) in triangulated
2-Calabi-Yau categories and related categories. In particular we construct a
new class of such categories related to preprojective algebras of non Dynkin
quivers associated with elements in the Coxeter group. This class of
2-Calabi-Yau categories contains the cluster categories and the stable
categories of preprojective algebras of Dynkin graphs as special cases. For
these 2-Calabi-Yau categories we construct cluster tilting objects associated
with each reduced expression. The associated quiver is described in terms of
the reduced expression. Motivated by the theory of cluster algebras, we
formulate the notions of (weak) cluster structure and substructure, and give
several illustrations of these concepts. We give applications to cluster
algebras and subcluster algebras related to unipotent groups, both in the
Dynkin and non Dynkin case.Comment: 49 pages. For the third version the presentation is revised,
especially Chapter III replaces the old Chapter III and I
Return to Sender : Confronting Lynching and Our Haunted Landscapes
This article considers a set of controversial images, primarily taken between 1880 and 1920, depicting lynchings and racial violence. Emory University has made these images publicly available, prompting some to worry that the collection will re-inflict trauma on those who suffered under racism in the United States. The articles asks, in part: if new initiatives in museums or other public spaces could help Americans to collectively confront their inner demons and move beyond the timeless repetition of trauma.
The article is available from Southern Changes: The Journal of the Southern Regional Council, 1978-2003
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Technical Review of Residential Programmable Communicating Thermostat Implementation for Title 24-2008
An approach to the preliminary evaluation of Closed Ecological Life Support System (CELSS) scenarios and control strategies
Life support systems for manned space missions are discussed. A scenario analysis method was proposed for the initial step of comparing possible partial or total recycle scenarios. The method is discussed in detail
Mutation in triangulated categories and rigid Cohen-Macaulay modules
We introduce the notion of mutation of -cluster tilting subcategories in a
triangulated category with Auslander-Reiten-Serre duality. Using this idea, we
are able to obtain the complete classifications of rigid Cohen-Macaulay modules
over certain Veronese subrings.Comment: 52 pages. To appear in Invent. Mat
Non-Gorenstein isolated singularities of graded countable Cohen-Macaulay type
In this paper we show a partial answer the a question of C. Huneke and G.
Leuschke (2003): Let R be a standard graded Cohen-Macaulay ring of graded
countable Cohen-Macaulay representation type, and assume that R has an isolated
singularity. Is R then necessarily of graded finite Cohen-Macaulay
representation type? In particular, this question has an affirmative answer for
standard graded non-Gorenstein rings as well as for standard graded Gorenstein
rings of minimal multiplicity. Along the way, we obtain a partial
classification of graded Cohen-Macaulay rings of graded countable
Cohen-Macaulay type.Comment: 15 Page
Automorphism groups of polycyclic-by-finite groups and arithmetic groups
We show that the outer automorphism group of a polycyclic-by-finite group is
an arithmetic group. This result follows from a detailed structural analysis of
the automorphism groups of such groups. We use an extended version of the
theory of the algebraic hull functor initiated by Mostow. We thus make
applicable refined methods from the theory of algebraic and arithmetic groups.
We also construct examples of polycyclic-by-finite groups which have an
automorphism group which does not contain an arithmetic group of finite index.
Finally we discuss applications of our results to the groups of homotopy
self-equivalences of K(\Gamma, 1)-spaces and obtain an extension of
arithmeticity results of Sullivan in rational homotopy theory
On Hausdorff dimension of the set of closed orbits for a cylindrical transformation
We deal with Besicovitch's problem of existence of discrete orbits for
transitive cylindrical transformations
where is an
irrational rotation on the circle \T and \varphi:\T\to\R is continuous,
i.e.\ we try to estimate how big can be the set
D(\alpha,\varphi):=\{x\in\T:|\varphi^{(n)}(x)|\to+\infty\text{as}|n|\to+\infty\}.
We show that for almost every there exists such that the
Hausdorff dimension of is at least . We also provide a
Diophantine condition on that guarantees the existence of
such that the dimension of is positive. Finally, for some
multidimensional rotations on \T^d, , we construct smooth
so that the Hausdorff dimension of is positive.Comment: 32 pages, 1 figur
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