3 citations · 6 across the 6 of their papers we have counts for
8 papers · 1 filter
Skew Clifford Algebras
Thomas Cassidy, Michaela Vancliff
We introduce a generalization, called a skew Clifford algebra, of a Clifford algebra, and relate these new algebras to the notion of graded skew Clifford algebra that was defined i…
Periodic free resolutions from twisted matrix factorizations
Thomas Cassidy, Andrew Conner, Ellen Kirkman +1
The notion of a matrix factorization was introduced by Eisenbud in the commutative case in his study of bounded (periodic) free resolutions over complete intersections. In this wor…
Quotients of Koszul algebras and 2-d-determined algebras
Thomas Cassidy, Christopher Phan
Vatne and Green & Marcos have independently studied the Koszul-like homological properties of graded algebras that have defining relations in degree 2 and exactly one other degree.…
Quadratic algebras with Ext algebras generated in two degrees
Thomas Cassidy
We show that there exist non-Koszul graded algebras that appear to be Koszul up to any given cohomological degree. For any integer m>2 we exhibit a non-commutative quadratic algebr…
Noncommutative Koszul Algebras from Combinatorial Topology
Thomas Cassidy, Christopher Phan, Brad Shelton
Associated to any uniform finite layered graph Gamma there is a noncommutative graded quadratic algebra A(Gamma) given by a construction due to Gelfand, Retakh, Serconek and Wilson…
The Yoneda algebra of a K_2 algebra need not be another K_2 algebra
Thomas Cassidy, Christopher Phan, Brad Shelton
The Yoneda algebra of a Koszul algebra or a D-Koszul algebra is Koszul. K_2 algebras are a natural generalization of Koszul algebras, and one would hope that the Yoneda algebra of…