Associative rings and algebras Rings with additional structure Concept
Differential graded algebra
Summary
A differential graded algebra, or dg algebra, is a graded algebra with a differential of degree one. The differential squares to zero and obeys a signed Leibniz rule. Forgetting the product it is a chain complex, and its cohomology is again a graded algebra. The de Rham complex of a smooth manifold, the singular cochains of a space with the cup product, and Koszul complexes are standard examples. Dg algebras are the basic objects of homological algebra with products and of rational homotopy theory.
Further reading
About this page
| Tag | GQVAXW5X09 |
|---|---|
| URI | m2://GQVAXW5X09 |
| Kind | concept |
| Writing | W0 stub |
| MSC | 16E45, 18G35 |
| Same as |
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