A survey on the Koszul homology algebra
Rachel N. Diethorn

TL;DR
This survey reviews classical and recent results on the structure of Koszul homology algebras of rings, highlighting their role in characterizing ring properties and discussing open questions in the field.
Contribution
It provides a comprehensive overview of the classical and recent developments in the study of Koszul homology algebras, emphasizing their applications and open problems.
Findings
Characterization of rings via Koszul homology algebra structure
Recent progress on Koszul algebras' homology structures
Open questions on the algebraic properties of Koszul homologies
Abstract
The Koszul homology algebra of a commutative local (or graded) ring tends to reflect important information about the ring and its properties. In fact, certain classes of rings are characterized by the algebra structure on their Koszul homologies. In this paper we survey some classical results on the Koszul homology algebras of such rings and highlight some applications. We report on recent progress on the Koszul homology algebras of Koszul algebras and examine some open questions on the topic.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Algebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology
