Searcharxiv⌕ Search

arXiv subjects

Chad R. Mangum

Publications and source records attributed to Chad R. Mangum.

5 recordsLinked to original sources
arXiv2025

The Nature of Reasoning in Theology, Philosophy, and Mathematics

This article supports the epistemological claim that sound human reasoning about ultimate knowledge is either foundational or circularly justified. In particular, questions which naturally arise in theology, philosophy, and related disciplines, to the extent that they rationally treat ultimate knowledge, are necessarily supported in one of these ways. Comparisons with, contrasts to, and analogies from mathematics are given to illustrate and enhance this central claim.

math.HO↗
arXiv2024

Schur-Weyl Duality for Toroidal Algebras of Type $A$

We state and prove an analog of the Schur-Weyl duality for a quotient of the classical $2$-toroidal Lie algebra of type $A$. We then provide a method to extend this duality to the $m$-toroidal case, $m > 2$.

math.RT↗
arXiv2018

Bosonic free field realization of twisted 2-toroidal Lie algebras

Using free fields, we construct a bosonic realization of toroidal Lie algebras of type $A_{2n-1}, A_{2n}, D_{n+1}, D_4$ which are twisted by a Dynkin diagram automorphism. This realization is based upon the recently found Moody-Rao-Yokonuma-like presentation. In particular, our construction contains the first bosonic realization of the twisted affine algebra $D_4^{(3)}$.

math.RT↗
arXiv2016

On realization of some twisted toroidal Lie algebras

Toroidal Lie algebras are generalizations of affine Lie algebras. In 1990, Moody, Rao and Yokonuma gave a presentation for untwisted toroidal Lie algebras. In this paper we give a presentation for the twisted toroidal Lie algebras of type $A$ and $D$ constructed by Fu and Jiang.

math.RT↗