arXiv subjects

Puiman Ng

Publications and source records attributed to Puiman Ng.

3 recordsLinked to original sources

arXiv2012

Almost split sequences and approximations

Let A be an exact category, that is, an extension-closed full subcategory of an abelian category. Firstly, we give some necessary and sufficient conditions for A to have almost split sequences. Then, we study when an almost split sequence in A induces an almost split sequence in an exact subcategory C of A. In case A has almost split sequences and C is Hom-finite Krull-Schmidt, this provides a necessary and sufficient condition for C to have almost split sequences. Finally, we show two applications of these results.

math.CT↗

arXiv2010

A characterization of torsion theories in the cluster category of Dynkin type A_{\infty}

Let D be the cluster category of Dynkin type A_{\infty}. This paper provides a bijection between torsion theories in D and certain configurations of arcs connecting non-neighbouring integers.

math.RT↗

arXiv2009

Existence of Auslander-Reiten sequences in subcategories

This paper studies the existence of Auslander-Reiten sequences in subcategories of mod A, where A is a finite dimensional algebra over a field. The two main theorems give necessary and sufficient conditions for the existence of Auslander-Reiten sequences in subcategories. Let M be a subcategory of mod A closed under extensions and direct summands, and let X be an indecomposable module in M such that Ext^{1}(X, X') is not zero for some X' in M. Then the following are equivalent: (i) DTrX has a precover in the stable category of mod A, (ii) There exists an Auslander-Reiten sequence 0 --> U --> W --> X --> 0 in M. We also have the dual result of the above theorem.

math.RT↗