Free resolutions of algebras
Joe Chuang, Alastair King
TL;DR
This paper presents a method to construct free algebra resolutions for algebras defined by generators and relations, using combinatorial bracketings to build a differential graded algebra that is quasi-isomorphic to the original algebra.
Contribution
It introduces a combinatorial construction of free resolutions for algebras presented by generators and relations, utilizing bracketings in differential graded algebra.
Findings
Constructs explicit free resolutions for algebras
Uses combinatorial bracketings for resolution construction
Provides a differential graded algebra quasi-isomorphic to the original algebra
Abstract
Given an algebra A, presented by generators and relations, i.e. as a quotient of a tensor algebra by an ideal, we construct a free algebra resolution of A, i.e. a differential graded algebra which is quasi-isomorphic to A and which is itself a tensor algebra. The construction rests combinatorially on the set of bracketings that arise naturally in the description of a free contractible differential graded algebra with given generators.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Commutative Algebra and Its Applications