4 citations · 13 across the 9 of their papers we have counts for
9 papers
Support -tilting and 2-torsion pairs
Jordan McMahon
The theory of -tilting was introduced by Adachi--Iyama--Reiten; one of the main results is a bijection between support -tilting modules and torsion classes. We are able to ge…
Boundary Idempotents and -precluster-tilting categories
Jordan McMahon
The homological theory of Auslander-Platzeck-Todorov on idempotent ideals laid much of the groundwork for higher Auslander-Reiten theory, providing the key technical lemmas for bot…
Iyama's higher Auslander correspondence via the homological theory of idempotent ideals
Jordan McMahon
A celebrated result in representation theory is that of higher Auslander correspondence. Let an Artin algebra and a -cluster-tilting module. Iyama has shown that the end…
The combinatorics of tensor products of higher Auslander algebras of type
Jordan McMahon, Nicholas J. Williams
We consider maximal non--intertwining collections, which are a higher-dimensional version of the maximal non-crossing collections which give clusters of Plücker coordinates in t…
Higher gentle algebras
Jordan McMahon
We introduce higher gentle algebras. Our definition allows us to determine the singularity categories and subsequently show that higher gentle algebras are Iwanaga-Gorenstein. Unde…
Higher support tilting I: higher Auslander algebras of linearly oriented type
Jordan McMahon
For a path algebra over a quiver , there are bijections between the support-tilting modules of , torsion classes in and wide subcategories in $\mathrm{m…
Fabric idempotents and homological dimensions
Jordan McMahon
Over a finite-dimensonal algbera , simple -modules that have projective dimension one have special properties. For example, Geigle-Lenzing studied them in connection to homol…
Quiddity sequences for -frieze patterns
Jordan McMahon
The notion of a -frieze pattern was introduced by the author as a generalisation of the classical frieze patterns. In this article we describe connections between classes of…
Higher frieze patterns
Jordan McMahon
Frieze patterns have an interesting combinatorial structure, which has proven very useful in the study of cluster algebras. We introduce -frieze patterns, a natural generali…