71 research outputs found
Algebras stratified for all linear orders
In this paper we describe several characterizations of basic
finite-dimensional -algebras stratified for all linear orders, and
classify their graded algebras as tensor algebras satisfying some extra
property. We also discuss whether for a given preorder ,
, the category of -modules with
-filtrations, is closed under cokernels of
monomorphisms, and classify quasi-hereditary algebras satisfying this property.Comment: Final version accepted by Alg. Repn. Theor
Decomposition of modules over right uniserial rings
Dlab V, Ringel CM. Decomposition of modules over right uniserial rings. Mathematische Zeitschrift. 1972;129(3):207-230
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
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
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
A-D-E Quivers and Baryonic Operators
We study baryonic operators of the gauge theory on multiple D3-branes at the
tip of the conifold orbifolded by a discrete subgroup Gamma of SU(2). The
string theory analysis predicts that the number and the order of the fixed
points of Gamma acting on S^2 are directly reflected in the spectrum of
baryonic operators on the corresponding quiver gauge theory constructed from
two Dynkin diagrams of the corresponding type. We confirm the prediction by
developing techniques to enumerate baryonic operators of the quiver gauge
theory which includes the gauge groups with different ranks. We also find that
the Seiberg dualities act on the baryonic operators in a non-Abelian fashion.Comment: 46 pages, 17 figures; v2: minor corrections, note added in section 1,
references adde
On the unitarization of linear representations of primitive partially ordered sets
We describe all weights which are appropriated for the unitarization of
linear representations of primitive partially ordered sets of finite type
Tree modules and counting polynomials
We give a formula for counting tree modules for the quiver S_g with g loops
and one vertex in terms of tree modules on its universal cover. This formula,
along with work of Helleloid and Rodriguez-Villegas, is used to show that the
number of d-dimensional tree modules for S_g is polynomial in g with the same
degree and leading coefficient as the counting polynomial A_{S_g}(d, q) for
absolutely indecomposables over F_q, evaluated at q=1.Comment: 11 pages, comments welcomed, v2: improvements in exposition and some
details added to last sectio
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