Differential graded algebra

<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a> – particularly in <a href="/facts/Homological_algebra/Jfm8w52l">homological algebra</a>, <a href="/facts/Algebraic_topology/2wA8yrjT">algebraic topology</a>, and <a href="/facts/Algebraic_geometry/rh7RHVp3">algebraic geometry</a> – a differential graded algebra (or DGA, or DG algebra) is an <a href="/facts/Algebra/nMdqczjo">algebraic structure</a> often used to capture information about a <a href="/facts/Topological_space/v2ut7CbK">topological</a> or <a href="/facts/Geometry/wTQf5ffQ">geometric</a> space. Explicitly, a differential graded algebra is a <a href="/facts/Graded_algebra/AIUjkSaP">graded</a> <a href="/facts/Associative_algebra/DRfoF6KV">associative algebra</a> with a <a href="/facts/Chain_complex/YAlchtCT">chain complex</a> structure that is compatible with the <a href="/facts/Algebra_over_a_field/8T8ulWJb">algebra</a> structure. 
</p><p>In geometry, the <a href="/facts/De_rham_cohomology/4qGKeJq0">de Rham algebra</a> of <a href="/facts/Differential_forms/T9gyHtMv">differential forms</a> on a <a href="/facts/Manifold/rXPERJtu">manifold</a> has the structure of a differential graded algebra, and it encodes the <a href="/facts/De_Rham_cohomology/4qGKeJq0">de Rham cohomology</a> of the manifold. In algebraic topology, the <a href="/facts/Singular_cohomology/J7FJzTNh">singular cochains</a> of a topological space form a DGA encoding the <a href="/facts/Cohomology/J7FJzTNh">singular cohomology</a>. Moreover, American mathematician <a href="/facts/Dennis_Sullivan/qb6wrKXr">Dennis Sullivan</a> developed a DGA to encode the <a href="/facts/Rational_homotopy_type/b91f4L7z">rational homotopy type</a> of topological spaces.
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Differential graded algebra open-in-new

Differential graded algebra