dc.contributor.author | Nafari, Manizheh | en_US |
dc.date.accessioned | 2011-10-11T20:49:03Z | |
dc.date.available | 2011-10-11T20:49:03Z | |
dc.date.issued | 2011-10-11 | |
dc.date.submitted | January 2011 | en_US |
dc.identifier.other | DISS-11335 | en_US |
dc.identifier.uri | http://hdl.handle.net/10106/6190 | |
dc.description.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. | en_US |
dc.description.sponsorship | Vancliff, Michaela | en_US |
dc.language.iso | en | en_US |
dc.publisher | Mathematics | en_US |
dc.title | Regular Algebras Related To Regular Graded Skew Clifford Algebras Of Low Global Dimension | en_US |
dc.type | Ph.D. | en_US |
dc.contributor.committeeChair | Vancliff, Michaela | en_US |
dc.degree.department | Mathematics | en_US |
dc.degree.discipline | Mathematics | en_US |
dc.degree.grantor | University of Texas at Arlington | en_US |
dc.degree.level | doctoral | en_US |
dc.degree.name | Ph.D. | en_US |