Expand all Collapse all | Results 1 - 6 of 6 |
1. CJM 2014 (vol 67 pp. 28)
Bounded Derived Categories of Infinite Quivers: Grothendieck Duality, Reflection Functor We study bounded derived categories of the category of representations of infinite quivers over a ring $R$. In case $R$ is a commutative noetherian ring with a dualising complex, we investigate an equivalence similar to Grothendieck duality for these categories, while a notion of dualising complex does not apply to them. The quivers we consider are left, resp. right, rooted quivers that are either noetherian or their opposite are noetherian. We also consider reflection functor and generalize a result of Happel to noetherian rings of finite global dimension, instead of fields.
Keywords:derived category, Grothendieck duality, representation of quivers, reflection functor Categories:18E30, 16G20, 18E40, 16D90, 18A40 |
2. CJM 2012 (vol 64 pp. 1222)
Normality of Maximal Orbit Closures for Euclidean Quivers Let $\Delta$ be an Euclidean quiver. We prove that the closures of
the maximal orbits in the varieties of representations of $\Delta$
are normal and Cohen--Macaulay (even complete intersections).
Moreover, we give a generalization of this result for the tame
concealed-canonical algebras.
Keywords:normal variety, complete intersection, Euclidean quiver, concealed-canonical algebra Categories:16G20, 14L30 |
3. CJM 2009 (vol 61 pp. 315)
Injective Representations of Infinite Quivers. Applications In this article we study injective representations of infinite
quivers. We classify the indecomposable injective representations of
trees and describe Gorenstein injective and projective
representations of barren trees.
Categories:16G20, 18A40 |
4. CJM 2007 (vol 59 pp. 1260)
Generic Extensions and Canonical Bases for Cyclic Quivers We use the monomial basis theory developed by Deng and Du to
present an elementary algebraic construction of the canonical
bases for both the Ringel--Hall algebra of a cyclic quiver and the
positive part $\bU^+$ of the quantum affine $\frak{sl}_n$. This
construction relies on analysis of quiver representations and the
introduction of a new integral PBW-like basis for the Lusztig
$\mathbb Z[v,v^{-1}]$-form of~$\bU^+$.
Categories:17B37, 16G20 |
5. CJM 2006 (vol 58 pp. 180)
Infinite Dimensional Representations of Canonical Algebras The
aim of this paper is to extend the structure theory for infinitely
generated modules over tame hereditary algebras to the more
general case of modules over concealed canonical algebras. Using
tilting, we may assume that we deal with canonical algebras. The
investigation is centered around the generic and the Pr\"{u}fer
modules, and how other modules are determined by these
modules.
Categories:16D70, 16D90, 16G20, 16G60, 16G70 |
6. CJM 1999 (vol 51 pp. 488)
Homological Aspects of Semigroup Gradings on Rings and Algebras This article studies algebras $R$ over a simple artinian ring $A$,
presented by a quiver and relations and graded by a semigroup $\Sigma$.
Suitable semigroups often arise from a presentation of $R$.
Throughout, the algebras need not be finite dimensional. The graded
$K_0$, along with the $\Sigma$-graded Cartan endomorphisms and Cartan
matrices, is examined. It is used to study homological properties.
A test is found for finiteness of the global dimension of a
monomial algebra in terms of the invertibility of the Hilbert
$\Sigma$-series in the associated path incidence ring.
The rationality of the $\Sigma$-Euler characteristic, the Hilbert
$\Sigma$-series and the Poincar\'e-Betti $\Sigma$-series is studied
when $\Sigma$ is torsion-free commutative and $A$ is a division ring.
These results are then applied to the classical series. Finally, we
find new finite dimensional algebras for which the strong no loops
conjecture holds.
Categories:16W50, 16E20, 16G20 |