Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 1 of 1
Full-Text Articles in Physical Sciences and Mathematics
Pbw Deformations Of Artin-Schelter Regular Algebras And Their Homogenizations, Jason D. Gaddis
Pbw Deformations Of Artin-Schelter Regular Algebras And Their Homogenizations, Jason D. Gaddis
Theses and Dissertations
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 are not necessarily graded. In particular, we define an algebra to be essentially regular of dimension d if its homogenization is regular of dimension d+1. Essentially regular algebras are described and it is shown that that they are equivalent to PBW deformations of regular algebras. In order to classify essentially regular algebras we introduce a modified version of matrix congruence, called sf-congruence, which is equivalent to …