A graded algebra equipped with a degree-one differential satisfying and . Its cohomology inherits a graded algebra structure. In rational homotopy, a Sullivan minimal model is a free graded-commutative differential graded algebra with decomposable generator differentials.
A commutative differential graded algebra has multiplication and a degree-one differential with and . Over , its free algebra on graded generators is polynomial on even-degree generators and exterior on odd-degree generators. Rational rational polynomial differential forms on a space supply such an algebra, modelled up to quasi-isomorphism by a Sullivan minimal model.
Articles by others on the same topic
Differential graded algebra (DGA) is a mathematical structure that combines concepts from algebra and topology, particularly in the context of homological algebra and algebraic topology. A DGA consists of a graded algebra equipped with a differential that satisfies certain properties. Here’s a more detailed breakdown of the components and properties: ### Components of a Differential Graded Algebra 1.