arXiv subjects

Annette Pilkington

Publications and source records attributed to Annette Pilkington.

3 recordsLinked to original sources

arXiv2021

Subregular J-Rings of the Finite Irreducible Coxeter Systems

In previous papers, the author showed that in many cases of interest there exists an isomorphism between certain path algebras related to the structure of the subregular J-rings of Coxeter systems and matrix rings over a free product of rings. For the finite irreducible Coxeter systems, the application of the isomorphism theorems was straightforward in all but a few cases. In this paper we show how the isomorphism theorems can be applied to show that the path algebras in the remaining cases are isomorphic to a direct sum of matrix rings over the rational numbers or over a direct product of field extensions of the rational numbers.

math.RA↗

arXiv2011

On The Weak Order Of Orthogonal Groups

A structure of a complete lattice (in the sense of a poset) is defined on the underlying set of the orhtogonal group of a real Euclidean space, by a construction analogous to that of the weak order of a Coxeter system in terms of its root system. This gives rise to a complte rootoid in the sense of Dyer, with the orthogonal group as underlying group.

math.GR↗

arXiv2011

Highest Weight Categories For Number Rings

This paper examines the concept of a stratified exact category in the context of number rings and corresponding Galois groups. BGG reciprocity and duality are proven for these categories making them highest weight categories. The strong connections between the structure of the category and ramification in the ring are explored.

math.RT↗