Graded identities of matrix algebras and the universal graded algebra

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

On the graded identities of the Grassmann algebra∗

We survey the results concerning the graded identities of the infinite dimensional Grassmann algebra. 2010 MSC: 16R10, 16P90, 16S10, 16W50

Hz-algebra Spectra Are Differential Graded Algebras

We construct Quillen equivalences on the Quillen model categories of rings, modules and algebras over Z-graded chain complexes and HZ-module spectra. A Quillen equivalence of Quillen model categories is the most highly structured notion of equivalence between homotopy theories. We use these equivalences in turn to produce algebraic models for rational stable model categories.

The G-graded Identities of the Grassmann Algebra

Let G be a finite abelian group with identity element 1G and L = ⊕ g∈G L g be an infinite dimensional G-homogeneous vector space over a field of characteristic 0. Let E = E(L) be the Grassmann algebra generated by L. It follows that E is a G-graded algebra. Let |G| be odd, then we prove that in order to describe any ideal of G-graded identities of E it is sufficient to deal with G′-grading, whe...