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

gradation or grading. A graded module is defined similarly (see below for the precise definition). It generalizes graded vector spaces. A graded module that is...

}I^{n}M/I^{n+1}M} . A differential graded module, differential graded Z {\displaystyle \mathbb {Z} } -module or DG-module is a graded module M {\displaystyle...

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

are endowed with the additional structure of a differential graded Z {\displaystyle \mathbb {Z} } -module. In detail, this means that Hom ⁡ ( A , B ) {\displaystyle...

after finitely many steps. Graded A graded module is a module with a decomposition as a direct sum M = ⨁x Mx over a graded ring R = ⨁x Rx such that RxMy...

the module Ω S / R {\displaystyle \Omega _{S/R}} of differentials in different, but equivalent ways. An R-linear derivation on S is an R-module homomorphism...

In mathematics, a D-module is a module over a ring D of differential operators. The major interest of such D-modules is as an approach to the theory of...

resolution of the differential graded algebra ( B ∙ , 0 ) {\displaystyle (B_{\bullet },0)} where B ∙ {\displaystyle B_{\bullet }} is the graded algebra with...

+ 1 ∘ d m = 0 {\displaystyle d_{m+1}\circ d_{m}=0} . A differential graded algebra is a graded algebra A {\textstyle A} with a linear derivation d : A...

Clifford algebra Cluster algebra Dendriform algebra Differential graded algebra Differential graded Lie algebra Exterior algebra F-algebra Filtered algebra...

Buchsbaum–Eisenbud acyclicity criterion Differential graded module "Graph complex". Bott, Raoul; Tu, Loring W. (1982), Differential Forms in Algebraic Topology,...

^{\bullet }{\mathfrak {g}}\otimes C^{\infty }(M)} considered as a differential graded module over the Lie algebra g {\displaystyle {\mathfrak {g}}} : K ∙ ...

of the module when r is the rank of the module. differential A differential graded module or dg-module is a graded module with a differential. direct...

{\mathcal {J}}_{k,n}}} spans the space of differential k-forms in a manifold M of dimension n, when viewed as a module over the ring C∞(M) of smooth functions...

geometry, graded manifolds are extensions of the concept of manifolds based on ideas coming from supersymmetry and supercommutative algebra. Both graded manifolds...

defines an OX-module (called an associated sheaf) in a natural way. Similarly, if R is a graded ring and X is the Proj of R, then any graded module defines...

graded rings, differential graded rings). Algebras over the so-called commutative operad are commutative algebras, i.e., commutative (possibly graded...

rational numbers Q. Assume we have a graded supercommutative ring X, so that ab = (−1)deg(a)deg (b)ba, with a differential d, with d(ab) = d(a)b + (−1)deg(a)ad(b))...

and is in fact a differential. In this setting, k {\displaystyle k} is viewed as a trivial g {\displaystyle {\mathfrak {g}}} -module while k ∼ Λ 0 g ∗...

R_{-1}\xrightarrow {s} R_{0}\xrightarrow {p} A\to 0} Then, by taking the differential graded module of derivations ( Der ( R ∙ ) , d ) {\displaystyle ({\text{Der}}(R_{\bullet...

differential graded category A differential graded category is a category whose Hom sets are equipped with structures of differential graded modules....

exterior algebra can be defined for modules over a commutative ring. In particular, the algebra of differential forms in k {\displaystyle k} variables...

resolution in which the free modules Ei may be graded in such a way that the di and ε are graded linear maps. Among these graded free resolutions, the minimal...

naturally to the setting of graded commutative algebra, allowing for a natural foundation of calculus on supermanifolds, graded manifolds and associated...

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...

modules is injective. Every left injective module over a left Noetherian module can be decomposed as a direct sum of indecomposable injective modules...

A Trusted Platform Module (TPM) is a secure cryptoprocessor that implements the ISO/IEC 11889 standard. Common uses are verifying that the boot process...

to the degree one graded piece of the abutment H 1(A). Because the spectral sequence lies in the first quadrant, the degree one graded piece is equal to...

Temperley-Lieb algebra. A differential graded algebra is an associative algebra together with a grading and a differential. For example, the de Rham algebra...