RESEARCH COMMONS
LIBRARY

Regular Algebras Related To Regular Graded Skew Clifford Algebras Of Low Global Dimension

ResearchCommons/Manakin Repository

Regular Algebras Related To Regular Graded Skew Clifford Algebras Of Low Global Dimension

Show full item record

Title: Regular Algebras Related To Regular Graded Skew Clifford Algebras Of Low Global Dimension
Author: Nafari, Manizheh
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.
URI: http://hdl.handle.net/10106/6190
Date: 2011-10-11

Files in this item

Files Size Format View
Nafari_uta_2502D_11335.pdf 402.6Kb PDF View/Open

This item appears in the following Collection(s)

Show full item record

Browse

My Account

Statistics

About Us