Graded isomorphisms on upper block triangular matrix algebras

Graded triangular algebras

Ela Graded Triangular Algebras

The structure of graded triangular algebras T of arbitrary dimension are studied in this paper. This is motivated in part for the important role that triangular algebras play in the study of oriented graphs, upper triangular matrix algebras or nest algebras. It is shown that T decomposes as T = U + ( ∑ i∈I Ti), where U is an R-submodule contained in the 0-homogeneous component and any Ti a well...

Involutions on 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...

Factorization of Block Triangular Matrix Functions in Wiener Algebras on Ordered Abelian Groups

The notion of Wiener-Hopf type factorization is introduced in the abstract framework of Wiener algebras of matrix-valued functions on connected compact abelian groups. Factorizations of 2 x 2 block triangular matrix functions with elementary functions on the main diagonal are studied in detail. A conjectl,lre is formulated concerning characterization of dual groups with the property that every ...