3 citations · 11 across the 7 of their papers we have counts for
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Splitting Algebras II: The Cohomology Algebra
Brad Shelton
Gelfand, Retakh, Serconek and Wilson, in \cite{GRSW}, defined a graded algebra attached to any finite ranked poset - a generalization of the universal algebra of pseudo-r…
Splitting Algebras: Koszul, Cohen-Macaulay and Numerically Koszul
Tyler Kloefkorn, Brad Shelton
We study a finite dimensional quadratic graded algebra R defined from a finite ranked poset. This algebra has been central to the study of the splitting algebra of the poset, A, as…
factors of Koszul algebras and applications to face rings
Andrew Conner, Brad Shelton
Generalizing the notion of a Koszul algebra, a graded k-algebra A is K2 if its Yoneda algebra is generated as an algebra in cohomology degrees 1 and 2. We prove a strong theorem ab…
The Koszul property as a topological invariant and a measure of singularities
Hal Sadofsky, Brad Shelton
Cassidy, Phan and Shelton associate to any regular cell complex X a quadratic K-algebra R(X). They give a combinatorial solution to the question of when this algebra is Koszul. The…
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…