2,205 research outputs found
The strong global dimension of piecewise hereditary algebras
Let T be a tilting object in a triangulated category equivalent to the
bounded derived category of a hereditary abelian category with finite
dimensional homomorphism spaces and split idempotents. This text investigates
the strong global dimension, in the sense of Ringel, of the endomorphism
algebra of T. This invariant is expressed using the infimum of the lengths of
the sequences of tilting objects successively related by tilting mutations and
where the last term is T and the endomorphism algebra of the first term is
quasi-tilted. It is also expressed in terms of the hereditary abelian
generating subcategories of the triangulated category.Comment: Final published version. After refereeing, historical considerations
were added and the length of the article was reduced: Introduction and
Section 1 were reformulated; Subsection 2.1 was moved to Section 1 (with an
abridged proof); Subsection 3.2 was reformulated (with an abridged proof);
The proof in A.5 was rewritten (now shorter); And minor rewording was
processed throughout the articl
On multigraded generalizations of Kirillov-Reshetikhin modules
We study the category of Z^l-graded modules with finite-dimensional graded
pieces for certain Z+^l-graded Lie algebras. We also consider certain Serre
subcategories with finitely many isomorphism classes of simple objects. We
construct projective resolutions for the simple modules in these categories and
compute the Ext groups between simple modules. We show that the projective
covers of the simple modules in these Serre subcategories can be regarded as
multigraded generalizations of Kirillov-Reshetikhin modules and give a
recursive formula for computing their graded characters
Towards a Convenient Category of Topological Domains
We propose a category of topological spaces that promises to be convenient for the purposes of domain theory as a mathematical theory for modelling computation. Our notion of convenience presupposes the usual properties of domain theory, e.g. modelling the basic type constructors, fixed points, recursive types, etc. In addition, we seek to model parametric polymorphism, and also to provide a flexible toolkit for modelling computational effects as free algebras for algebraic theories. Our convenient category is obtained as an application of recent work on the remarkable closure conditions of the category of quotients of countably-based topological spaces. Its convenience is a consequence of a connection with realizability models
A Convenient Category of Domains
We motivate and define a category of "topological domains",
whose objects are certain topological spaces, generalising
the usual -continuous dcppos of domain theory.
Our category supports all the standard constructions of domain theory,
including the solution of recursive domain equations. It also
supports the construction of free algebras for (in)equational
theories, provides a model of parametric polymorphism,
and can be used as the basis for a theory of computability.
This answers a question of Gordon Plotkin, who asked
whether it was possible to construct a category of domains
combining such properties
- …