51 citations · 96 across the 34 of their papers we have counts for
41 papers
The Supertrace Defect of a Graded Endomorphism
Esma Dirican Erdal, Atabey Kaygun
Motivated by Igusa's relation between relative cyclic homology and the logarithm of the graded Cartan determinant, we isolate the homological step behind the passage from logarithm…
Signed Euler--Smith Profiles of Graded Algebras
Atabey Kaygun
Matrix Hilbert series retain local elementary-divisor data that their determinants discard. For locally finite positively graded elementary algebras whose vertex simples are of typ…
Local Smith Profiles of Twisted Calabi--Yau Algebras
Atabey Kaygun
The matrix Hilbert series of a locally finite elementary twisted Calabi--Yau algebra is the inverse of a matrix polynomial. The Smith normal form of this polynomial over the power…
Combinatorial Models for Linear Homotopy Theories
Atabey Kaygun
For a field of characteristic , we compare -linear chain complexes, semisimplicial vector spaces, augmented semisimplicial vector spaces, semicubical vector spaces, and a…
Arboreal Objects and Their Homotopy Theory
Atabey Kaygun
We construct a category $\OrdFor$ as an arboreal extension of , whose morphisms are ordered forests composed by grafting. We define a full functor $π\co…
Geometric Rigidity in Moduli Stacks of Algebras
Atabey Kaygun
We study quadratic moduli schemes of algebra laws on a fixed vector space under the transport-of-structure action of on . We construct an intr…