AN ALGORITHM FOR COMPUTING GRADED ALGEBRAS by Vaughanlee, M

AN OBSTRUCTION TO GENERALIZING SUPERALGEBRAS by Hannabuss, K

“…It is shown that a G-graded algebra in which xy is a scalar multiple of yx is just a twisted version of a Z2-graded superalgebra.…”

Formality in generalized Kähler geometry by Cavalcanti, G

“…This is done by showing that a certain differential graded algebra associated to a generalized complex manifold is formal in the generalized Kahler case, while it is never formal for a generalized complex structure on a nilpotent Lie algebra.…”

On the algebra of cornered Floer homology by Douglas, C, Manolescu, C

“…Bordered Floer homology associates to a parametrized oriented surface a certain differential graded algebra. We study the properties of this algebra under splittings of the surface. …”

Geometric invariant theory for graded unipotent groups and applications by Berczi, G, Doran, B, Hawes, T, Kirwan, FC

“…Given any action of U on a projective variety X extending to an action of U which is linear with respect to an ample line bundle on X, then provided that one is willing to replace the line bundle with a tensor power and to twist the linearisation of the action of U by a suitable (rational) character, and provided an additional condition is satisfied which is the analogue of the condition in classical GIT that there should be no strictly semistable points for the action, we show that the U-invariants form a finitely generated graded algebra; moreover the natural morphism from the semistable subset of X to the enveloping quotient is surjective and expresses the enveloping quotient as a geometric quotient of the semistable subset. …”

Elementary states, supergeometry and twistor theory by Pilato, A, Pilato, Alejandro

“…</p> <p>A supermanifold is a ringed space consisting of an underlying classical manifold and an augmented sheaf of <strong>Z</strong>₂-graded algebras locally isomorphic to an exterior algebra. …”