76 research outputs found
Algebraic K-theory of endomorphism rings
We establish formulas for computation of the higher algebraic -groups of
the endomorphism rings of objects linked by a morphism in an additive category.
Let be an additive category, and let Y\ra X be a covariant
morphism of objects in . Then for all , where is the
quotient ring of the endomorphism ring of modulo the
ideal generated by all those endomorphisms of which factorize through .
Moreover, let be a ring with identity, and let be an idempotent element
in . If is homological and has a finite projective resolution
by finitely generated projective -modules, then for all . This reduces calculations of the higher
algebraic -groups of to those of the quotient ring and the corner
ring , and can be applied to a large variety of rings: Standardly
stratified rings, hereditary orders, affine cellular algebras and extended
affine Hecke algebras of type .Comment: 21 pages. Representation-theoretic methods are used to study the
algebraic K-theory of ring
Derived Categories of Coherent Sheaves and Triangulated Categories of Singularities
In this paper we establish an equivalence between the category of graded
D-branes of type B in Landau-Ginzburg models with homogeneous superpotential W
and the triangulated category of singularities of the fiber of W over zero. The
main result is a theorem that shows that the graded triangulated category of
singularities of the cone over a projective variety is connected via a fully
faithful functor to the bounded derived category of coherent sheaves on the
base of the cone. This implies that the category of graded D-branes of type B
in Landau-Ginzburg models with homogeneous superpotential W is connected via a
fully faithful functor to the derived category of coherent sheaves on the
projective variety defined by the equation W=0.Comment: 26 pp., LaTe
The double Ringel-Hall algebra on a hereditary abelian finitary length category
In this paper, we study the category of semi-stable
coherent sheaves of a fixed slope over a weighted projective curve. This
category has nice properties: it is a hereditary abelian finitary length
category. We will define the Ringel-Hall algebra of and
relate it to generalized Kac-Moody Lie algebras. Finally we obtain the Kac type
theorem to describe the indecomposable objects in this category, i.e. the
indecomposable semi-stable sheaves.Comment: 29 page
Krull Dimension of Tame Generalized Multicoil Algebras
We determine the Krull dimension of the module category of finite dimensional tame generalized multicoil algebras over an algebraically closed field, which are domestic
Recollements of Module Categories
We establish a correspondence between recollements of abelian categories up
to equivalence and certain TTF-triples. For a module category we show,
moreover, a correspondence with idempotent ideals, recovering a theorem of
Jans. Furthermore, we show that a recollement whose terms are module categories
is equivalent to one induced by an idempotent element, thus answering a
question by Kuhn.Comment: Comments are welcom
Categorical Tinkertoys for N=2 Gauge Theories
In view of classification of the quiver 4d N=2 supersymmetric gauge theories,
we discuss the characterization of the quivers with superpotential (Q,W)
associated to a N=2 QFT which, in some corner of its parameter space, looks
like a gauge theory with gauge group G. The basic idea is that the Abelian
category rep(Q,W) of (finite-dimensional) representations of the Jacobian
algebra should enjoy what we call the Ringel
property of type G; in particular, rep(Q,W) should contain a universal
`generic' subcategory, which depends only on the gauge group G, capturing the
universality of the gauge sector. There is a family of 'light' subcategories
, indexed by points , where
is a projective variety whose irreducible components are copies of
in one--to--one correspondence with the simple factors of G.
In particular, for a Gaiotto theory there is one such family of
subcategories, , for each maximal degeneration of
the corresponding surface , and the index variety may be identified
with the degenerate Gaiotto surface itself: generic light subcategories
correspond to cylinders, while closed-point subcategories to `fixtures'
(spheres with three punctures of various kinds) and higher-order
generalizations. The rules for `gluing' categories are more general that the
geometric gluing of surfaces, allowing for a few additional exceptional N=2
theories which are not of the Gaiotto class.Comment: 142 pages, 8 figures, 5 table
Lifting and restricting recollement data
We study the problem of lifting and restricting TTF triples (equivalently,
recollement data) for a certain wide type of triangulated categories. This,
together with the parametrizations of TTF triples given in "Parametrizing
recollement data", allows us to show that many well-known recollements of right
bounded derived categories of algebras are restrictions of recollements in the
unbounded level, and leads to criteria to detect recollements of general right
bounded derived categories. In particular, we give in Theorem 1 necessary and
sufficient conditions for a 'right bounded' derived category of a differential
graded(=dg) category to be a recollement of 'right bounded' derived categories
of dg categories. In Theorem 2 we consider the particular case in which those
dg categories are just ordinary algebras.Comment: 29 page
Sounds of Silence : The Reflexivity, Self-decentralization, and Transformation Dimensions of Silence at Work
This article explores silence as a phenomenon and practice in the workplace through a Buddhist-enacted lens where silence is intentionally encouraged. It brings forward a reconsideration of the roles of silence in organizations by proposing emancipatory dimensions of silence—reflexivity, self-decentralization, and transformation. Based on 54 interviews with employees and managers in a Vietnamese telecommunications organization, we discuss the dynamic nature of silence, and the possible coexistence of the constructive and the oppressive aspects of silence in a workplace spirituality context. Instead of studying silence as one-dimensional, we call for an integrated view and argue that studying silence requires consideration of the multiplicity of its interconnected dimensions. By considering silence as a relational and emerging processes constructed around its vagueness and uncertainties, our study reveals the many possible ways silence is organized and organizes and sheds light on silence as a marker of the complexities and paradoxes of organizational life
Die Krull-Gabriel-Dimension der endlich praesentierten Funktoren ueber Artin-Algebren und ihre Anwendung auf exakte Sequenzen
SIGLECopy held by FIZ Karlsruhe; available from UB/TIB Hannover / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman
- …