Buchsbaum-Eisenbud complexes of OI-modules
Nathan Fieldsteel, Uwe Nagel
TL;DR
This paper extends the theory of Buchsbaum-Eisenbud complexes to modules over commutative OI-algebras, demonstrating that these complexes retain key properties such as generic acyclicity and minimal free resolutions.
Contribution
It introduces a new framework for Buchsbaum-Eisenbud complexes in the context of OI-modules, preserving classical properties in this generalized setting.
Findings
OI-complexes are generically acyclic
They often provide width-wise minimal free resolutions
The classical properties of these complexes are retained in the OI setting
Abstract
We extend the theory of Koszul and Buchsbaum-Eisenbud complexes to modules over commutative OI-algebras and show that they still have the familiar properties of the classical complexes. In particular, the OI-complexes are generically acyclic and often provide width-wise minimal free resolutions.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Rings, Modules, and Algebras