Homological Associativity of Differential Graded Algebras and Gr\"obner Bases
Michael Nelson
TL;DR
This paper explores the associativity of multiplications on chain complexes over rings, introducing a homological approach and computational methods using Gr"obner bases to analyze associativity.
Contribution
It presents a novel homological framework and computational technique for detecting associativity in differential graded algebras.
Findings
Homology of the associator subcomplex detects associativity.
Gr"obner bases can be used to compute associators.
Provides new tools for studying algebraic structures on chain complexes.
Abstract
We investigate associativity of multiplications on chain complexes over commutative noetherian rings from two perspectives. First, we introduce a natural associator subcomplex and show how its homology can detect associativity. Second, we use Gr\"obner bases to compute associators.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology