## Graduation Semester and Year

2011

## Language

English

## Document Type

Dissertation

## Degree Name

Doctor of Philosophy in Mathematics

## Department

Mathematics

## First Advisor

Michaela Vancliff

## Abstract

M. Artin, W. Schelter, J. Tate, and M. Van den Bergh introduced the notion of non-commutative regular algebras, and classified regular algebras of global dimension 3 on degree-one generators by using geometry (i.e., point schemes) in the late 1980s. Recently, T. Cassidy and M. Vancliff generalized the notion of a graded Clifford algebra and called it a graded skew Clifford algebra.In this thesis, we prove that all classes of quadratic regular algebras of global dimension 3 contain graded skew Clifford algebras or Ore extensions of graded skew Clifford algebras of global dimension 2. We also prove that some regular algebras of global dimension 4 can be obtained from Ore extensions of regular graded skew Clifford algebras of global dimension 3. We also show that a certain subalgebra R of a regular graded skew Clifford algebra A is a twist of the polynomial ring if A is a twist of a regular graded Clifford algebra B. We have an example that demonstrates that this can fail when A is not a twist of B.

## Disciplines

Mathematics | Physical Sciences and Mathematics

## License

This work is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 4.0 International License.

## Recommended Citation

Nafari, Manizheh, "Regular Algebras Related To Regular Graded Skew Clifford Algebras Of Low Global Dimension" (2011). *Mathematics Dissertations*. 73.

https://mavmatrix.uta.edu/math_dissertations/73

## Comments

Degree granted by The University of Texas at Arlington