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...

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

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

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

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

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

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 =...

differential graded algebra is a graded associative algebra with an added chain complex structure that respects the algebra structure. A differential graded algebra...

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...

geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear...

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

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

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...

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...

extended to modules over a graded commutative algebra. This is the case of superconnections in supergeometry of graded manifolds and supervector bundles...

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...

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

compact complex tori, K3 surfaces are the Calabi–Yau manifolds (and also the hyperkähler manifolds) of dimension two. As such, they are at the center of...

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

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})\...

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...

model Flamelet generated manifold, a chemistry reduction technique Flux-gate magnetometer, a measuring instrument Functionally graded material, in materials...

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...

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

boundary, is a tamely graded Fréchet space, with any of the above graded structures. If M {\displaystyle M} is a compact smooth manifold and V → M {\displaystyle...

construction that produces a graded algebra out of a filtered algebra. If A {\displaystyle A} is a filtered algebra, then the associated graded algebra G ( A ) {\displaystyle...

A scuba manifold is a device incorporating one or more valves and one or more gas outlets with scuba regulator connections, used to connect two or more...

Canonical one-form, a special 1-form defined on the cotangent bundle T*M of a manifold M Canonical symplectic form, the exterior derivative of this form Canonical...