Browsing by Author "Ian Musson"

Infinitely Generated Clifford Algebras and Wedge Representations of gl∞|∞

Schleben, Bradford J. (2015-05-01)

The goal of this dissertation is to explore representations of $\mathfrak{gl}_{\infty|\infty}$ and associated Clifford superalgebras. The machinery utilized is motivated by developing an alternate superalgebra analogue to ...

Invariant Polynomials on Tensors Under the Action of a Product of Orthogonal Groups

Williams, Lauren Kelly (2013-08-01)

Let K be the product O(n1) × O(n2) × … × O(nr) of orthogonal groups. Let V be the r-fold tensor product of defining representations of each orthogonal factor. We compute a stable formula for the dimension of the K-invariant ...

PBW Deformations of Artin-Schelter Regular Algebras and Their Homogenizations

Gaddis, Jason D. (2013-05-01)

A central object in the study of noncommutative projective geometry is the (Artin-Schelter) regular algebra, which may be considered as a noncommutative version of a polynomial ring. We extend these ideas to algebras which ...

Restricting a Representation to a Principally Embedded Sl(2) Subalgebra

Lhou, Hassan (2016-08-01)

Fix n>2. Let s be a principally embedded sl(2)-subalgebra in sl(n). A special case of work by Jeb Willenbring and Gregg Zuckerman implies that there exists a positive integer b(n) such that for any finite dimensional ...

Some Results on Pseudo-Collar Structures on High-Dimensional Manifolds

Rolland, Jeffrey Joseph (2015-05-01)

In this dissertation we outline a partial reverse to Quilen's plus construction in the high-dimensional manifold categor. We show that for any orientable manifold N with fundamental group Q and any fintely presented ...