algebra. Both graded manifolds and supermanifolds are phrased in terms of sheaves of graded commutative algebras. However, graded manifolds are characterized...

the r-order jet manifold JrY of Y. A Lagrangian L can be introduced as an element of the variational bicomplex of the differential graded algebra O∗∞(Y)...

SUSY-manifold. SUSY-structure in dimension (1, k) is the same as odd contact structure. Superspace Supersymmetry Supergeometry Graded manifold Batalin–Vilkovisky...

a topological or geometric space. Explicitly, a differential graded algebra is a graded associative algebra with a chain complex structure that is compatible...

In mathematics, a differentiable manifold (also differential manifold) is a type of manifold that is locally similar enough to a vector space to allow...

differential graded category or DG category is a category whose morphism sets form differential graded Z {\displaystyle \mathbb {Z} } -modules. Graded manifold –...

Supergeometry is differential geometry of modules over graded commutative algebras, supermanifolds and graded manifolds. Supergeometry is part and parcel of many classical...

related field of supergeometry where they enter into the definitions of graded manifolds, supermanifolds and superschemes. Let K be a commutative ring. In most...

Poisson manifold is a smooth manifold endowed with a Poisson structure. The notion of Poisson manifold generalises that of symplectic manifold, which in...

compact manifolds of the same dimension, set up using the concept of the boundary (French bord, giving cobordism) of a manifold. Two manifolds of the same...

R)=\bigoplus _{i}H^{i}(X,R)} into a graded ring, called the cohomology ring of X {\displaystyle X} . It is graded-commutative in the sense that: u v =...

There are different descriptions of odd classical fields both on graded manifolds and supermanifolds. As above with classical fields, it is possible...

Cavern and Thyrsis's Cave) is a natural cavern located at SK09865496 in the Manifold Valley of the White Peak in Staffordshire, England. It is classified as...

bicomplex is a cochain complex of the differential graded algebra of exterior forms on jet manifolds of sections of a fiber bundle. Lagrangians and Euler–Lagrange...

Manifold injection is a mixture formation system for internal combustion engines with external mixture formation. It is commonly used in engines with spark...

In mathematics, an alternating 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...

to the top of the manifold so that they will be unobstructed when they are also pulled along. Yuasa successfully ascends the manifold, but Lemons’ umbilical...

model, an evolutionary model Flamelet generated manifold, a chemistry reduction technique Functionally graded material, in materials science Free Gaza Movement...

an algebraic variety V (which is nonsingular), or of a complex manifold, is the graded ring R ( V , K ) = R ( V , K V ) {\displaystyle R(V,K)=R(V,K_{V})\...

commutative graded ring, mimicking a theorem of Serre on Proj. Namely the category of quasicoherent sheaves of O-modules on a Proj of a commutative graded algebra...

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

geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of single variable calculus, vector calculus,...

study of quantum groups. Manifolds with a Poisson algebra structure are known as Poisson manifolds, of which the symplectic manifolds and the Poisson–Lie groups...

are isomorphic (as graded rings), where the analogous product on singular cohomology is the cup product. For any smooth manifold M, let R _ {\textstyle...

define integrands over curves, surfaces, solids, and higher-dimensional manifolds. The modern notion of differential forms was pioneered by Élie Cartan...

(4): 413–455. doi:10.24033/asens.1254. Kostant, Bertram (1977). "Graded manifolds, graded Lie theory, and prequantization". In: Differential Geometrical...

cover of a Fano manifold is compact, and so can only be a finite covering. However, we have just seen that the Todd genus of a Fano manifold must equal 1...

infinite-dimensional manifold and a real valued function on it. In the symplectic version, this is the free loop space of a symplectic manifold with the symplectic...

have the structure of a Z2-graded Hopf algebra. Likewise the representations of this Hopf algebra turn out to be Z2-graded comodules. This Hopf algebra...

{\displaystyle A+A^{*}} is not a Lie algebroid. Instead using the larger N-graded manifold T ∗ [ 2 ] A [ 1 ] = T ∗ [ 2 ] A ∗ [ 1 ] {\displaystyle T^{*}[2]A[1]=T^{*}[2]A^{*}[1]}...