homological algebra, algebraic topology, and algebraic geometry – a differential graded algebra (or DGA, or DG algebra) is an algebraic structure often...

mathematics, differential algebra is, broadly speaking, the area of mathematics consisting in the study of differential equations and differential operators...

is also a graded ring is called a graded algebra. A graded ring could also be viewed as a graded ⁠ Z {\displaystyle \mathbb {Z} } ⁠-algebra. The associativity...

abstract algebra and topology, a differential graded Lie algebra (or dg Lie algebra, or dgla) is a graded vector space with added Lie algebra and chain...

derivative gives the exterior algebra of differential forms on a manifold the structure of a differential graded algebra. The exterior derivative commutes...

(isomorphism classes of) certain algebraic objects called Sullivan minimal models, which are commutative differential graded algebras over the rational numbers...

In mathematics, especially homological algebra, a differential graded category, often shortened to dg-category or DG category, is a category whose morphism...

and the interior product acting on differential forms. Graded derivations of superalgebras (i.e. Z2-graded algebras) are often called superderivations...

commutative rings are replaced with derived versions such as differential graded algebras, commutative simplicial rings, or commutative ring spectra. From...

In algebra, a differential graded module, or dg-module, is a Z {\displaystyle \mathbb {Z} } -graded module together with a differential; i.e., a square-zero...

A differential graded algebra, DG-algebra or DGAlgebra is a graded algebra that is a differential graded module whose differential obeys the graded Leibniz...

algebra Differential graded algebra Differential graded Lie algebra Exterior algebra F-algebra Filtered algebra Flexible algebra Freudenthal algebra Functional-theoretic...

the graded cohomology algebra H A ∙ {\displaystyle HA^{\bullet }} which preserves the quasi-isomorphism structure of the original differential graded algebra...

into a commutative differential graded algebra. It also has a coalgebra structure inherited from the one on the exterior algebra. The hypercohomology...

representation theory, differential geometry, quantum statistical mechanics, quantum information, and quantum field theory. Operator algebras can be used to study...

algebra. A differential graded algebra is an associative algebra together with a grading and a differential. For example, the de Rham algebra Ω ( M ) =...

differential graded Lie algebra. To be a little more specific, the Jacobi identity only holds up to homotopy. Therefore, a differential graded Lie algebra can...

or noncommutative geometry a quantum differential calculus or noncommutative differential structure on an algebra A {\displaystyle A} over a field k {\displaystyle...

algebra is a Z-graded algebra for which xy = (−1)deg(x)deg(y)yx for all nonzero homogeneous elements x and y (i.e. it is an anticommutative algebra)...

minimal model, algebraic topology model of a differential graded algebra used in rational homotopy theory. Neron minimal model, algebraic geometry model...

mathematics, a graded Lie algebra is a Lie algebra endowed with a gradation which is compatible with the Lie bracket. In other words, a graded Lie algebra is a...

In mathematics, the Cartan model is a differential graded algebra that computes the equivariant cohomology of a space. Stefan Cordes, Gregory Moore, Sanjaye...

commutative rings, which provide local charts, are replaced by either differential graded algebras (over Q {\displaystyle \mathbb {Q} } ), simplicial commutative...

DGA, a series of planes built by Howard Aircraft Corporation Differential graded algebra Diglycolic acid Dissolved Gas Analysis, the analysis of gases...

algebra. One of the simplest examples of a differential graded algebra is the space of smooth differential forms on a smooth manifold, so that Sullivan...

universal enveloping algebra of the Lie algebra of a Lie group may be identified with the algebra of left-invariant differential operators on the group...

In algebra, the ring of polynomial differential forms on the standard n-simplex is the differential graded algebra: Ω poly ∗ ( [ n ] ) = Q [ t 0 , . ...

theory as the algebra of generalized Poisson brackets defined on differential forms. A Gerstenhaber algebra is a graded-commutative algebra with a Lie bracket...

In algebra, given a differential graded algebra A over a commutative ring R, the derived tensor product functor is − ⊗ A L − : D ( M A ) × D ( A M ) →...

pullback. Differential forms are part of the field of differential geometry, influenced by linear algebra. Although the notion of a differential is quite...