Graded differential geometry of graded matrix algebras

Graded Differential Geometry of Graded Matrix Algebras

We study the graded derivation-based noncommutative differential geometry of the Z2-graded algebra M(n|m) of complex (n+m)× (n+m)-matrices with the “usual block matrix grading” (for n 6= m). Beside the (infinite-dimensional) algebra of graded forms the graded Cartan calculus, graded symplectic structure, graded vector bundles, graded connections and curvature are introduced and investigated. In...

Involutions on graded matrix algebras

Recollement for Differential Graded Algebras

A recollement of triangulated categories describes one such category as being “glued together” from two others. This paper gives a precise criterion for the existence of a recollement of the derived category of a Differential Graded Algebra in terms of two other such categories.

The Geometry of A-graded Algebras

We study algebras k[x1, ..., xn]/I which admit a grading by a subsemigroup of N such that every graded component is a one-dimensional k-vector space. V.I. Arnold and coworkers proved that for d = 1 and n ≤ 3 there are only finitely many isomorphism types of such A-graded algebras, and in these cases I is an initial ideal (in the sense of Gröbner bases) of a toric ideal. In this paper it is show...

The Cotriple Resolution of Differential Graded Algebras

We consider the cotriple resolution of algebras over operads in differential graded modules. We focus, to be more precise, on the example of algebras over the differential graded Barratt-Eccles operad, and on the example of commutative alegbras. We prove that the geometric realization of the cotriple resolution (in the sense of model categories) gives a cofibrant resolution functor on these cat...