305 research outputs found
The first Hochschild cohomology group of a schurian cluster-tilted algebra
Given a cluster-tilted algebra B we study its first Hochschild cohomology group HH1(B) with coefficients in the B-B-bimodule B. We find several consequences when B is representation-finite, and also in the case where B is cluster-tilted of type Ã.Fil: Assem, Ibrahim. University of Sherbrooke; CanadáFil: Redondo, Maria Julia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentin
-cluster categories and -replicated algebras
Let A be a hereditary algebra over an algebraically closed field. We prove
that an exact fundamental domain for the m-cluster category of A is the m-left
part of the m-replicated algebra of A. Moreover, we obtain a
one-to-one correspondence between the tilting objects in the m-cluster category
(that is, the m-clusters) and those tilting -modules for which all non
projective-injective direct summands lie in the m-left part of .Comment: 28 pages, 2 figure
Cycle-finite module categories
We describe the structure of module categories of finite dimensional algebras
over an algebraically closed field for which the cycles of nonzero
nonisomorphisms between indecomposable finite dimensional modules are finite
(do not belong to the infinite Jacobson radical of the module category).
Moreover, geometric and homological properties of these module categories are
exhibited
Formation Damage Due to Iron Precipitation during Matrix Acidizing Treatments of Carbonate Reservoirs and Ways to Minimize it Using Chelating Agents
Iron precipitation during matrix acidizing treatments is a well-known problem. During matrix acidizing, successful iron control can be critical to the success of the treatment. Extensive literature review highlighted that no systematic study was conducted to determine where this iron precipitates, the factors that affect this precipitation, and the magnitude of the resulting damage.
Iron (III) precipitation occurs when acids are spent and the pH rises above 1, which can cause severe formation damage. Chelating agents are used during these treatments to minimize iron precipitation. Disadvantages of currently used chelating agents include limited solubility in strong acids, low thermal stability, and/or poor biodegradability.
In this study, different factors affecting iron precipitation in Indiana limestone rocks were examined. Two chelating agents, GLDA and HEDTA, were tested at different conditions to assess their iron control ability.
Results show that a significant amount of iron precipitated, producing a minimal or no gain in the final permeability, this indicated severe formation damage. The damage increased with the increase of the amount of iron in solution. When chelating agents were used, the amount of iron recovered depended on both chelate-to-iron mole ratio and the initial permeability of the cores. Calcium is chelated along with iron, which limits the effectiveness of chelating agents to control iron (III) precipitation. Acid solutions should be designed considering this important finding for more successful treatments
The Intrinsic Fundamental Group of a Linear Category
We provide an intrinsic definition of the fundamental group of a linear
category over a ring as the automorphism group of the fibre functor on Galois
coverings. If the universal covering exists, we prove that this group is
isomorphic to the Galois group of the universal covering. The grading deduced
from a Galois covering enables us to describe the canonical monomorphism from
its automorphism group to the first Hochschild-Mitchell cohomology vector
space.Comment: Final version, to appear in Algebras and Representation Theor
The derived category of surface algebras: the case of the torus with one boundary component
In this paper we refine the main result of a previous paper of the author
with Grimeland on derived invariants of surface algebras. We restrict to the
case where the surface is a torus with one boundary component and give an
easily computable derived invariant for such surface algebras. This result
permits to give answers to open questions on gentle algebras: it provides
examples of gentle algebras with the same AG-invariant (in the sense of
Avella-Alaminos and Geiss) that are not derived equivalent and gives a partial
positive answer to a conjecture due to Bobi\'nski and Malicki on gentle
-cycles algebras.Comment: 22 pages, a mistake concerning the computation of the mapping class
group has been fixed, version 3: 25 pages, to appear in Algebras and
Representation Theor
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
The solution of the quantum T-system for arbitrary boundary
We solve the quantum version of the -system by use of quantum
networks. The system is interpreted as a particular set of mutations of a
suitable (infinite-rank) quantum cluster algebra, and Laurent positivity
follows from our solution. As an application we re-derive the corresponding
quantum network solution to the quantum -system and generalize it to
the fully non-commutative case. We give the relation between the quantum
-system and the quantum lattice Liouville equation, which is the quantized
-system.Comment: 24 pages, 18 figure
Tilted algebras and short chains of modules
We provide an affirmative answer for the question raised almost twenty years
ago concerning the characterization of tilted artin algebras by the existence
of a sincere finitely generated module which is not the middle of a short
chain
Rigid and Schurian modules over cluster-tilted algebras of tame type
We give an example of a cluster-tilted algebra Λ with quiver Q, such that the associated cluster algebra A(Q) has a denominator vector which is not the dimension vector of any indecomposable Λ-module. This answers a question posed by T. Nakanishi. The relevant example is a cluster-tilted algebra associated with a tame hereditary algebra. We show that for such a cluster-tilted algebra Λ, we can write any denominator vector as a sum of the dimension vectors of at most three indecomposable rigid Λ-modules. In order to do this it is necessary, and of independent interest, to first classify the indecomposable rigid Λ-modules in this case
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