Mathematics Colloquium

Thursday, October 27

Time: 3:35 p.m. — 4:30 p.m.

Location: Science Center Room 323

Tags:  Arts and Sciences, Colloquia, Mathematics, Sciences

Cost:  Free

Speaker: Dr. Manizheh Nafari, Central State University

Host: Muhammad Usman

Title: (Regular) Graded Skew Clifford Algebras of Low Global Dimension

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 1980's. In 2010, T. Cassidy and M. Vancliff generalized the notion of a graded Clifford algebra and called it a graded skew Clifford algebra.

In this talk, 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 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.

Refreshments are available at 3:00 PM in SC 313F.

The department colloquia are held every Thursday (excluding holidays) at 3:35 pm in room SC 323 unless otherwise noted. All are invited to attend. 

Contact Information:

Name:  Paul Eloe
Email:  peloe1@udayton.edu