We show how the Connes–Moscovici bialgebroid construction naturally provides universal objects for Lie algebras acting on non-commutative algebras. As a supplement, we see these interact with study of flat bimodule connections.

In this paper, we establish the Pexiderized stability of coboundaries and cocycles and use them to investigate the Hyers–Ulam stability of some functional equations. We prove that for each Banach algebra A, Banach A-bimodule X and positive integer n, H n (A, X) = 0 if and only if the n-th cohomology group approximately vanishes.

Let Λ be a left and right Artin ring and ΛωΛ a faithfully balanced selforthogonal bimodule. We give a sufficient condition that the injective dimension of ωΛ is finite implies that of Λω is also finite.  2003 Elsevier Science (USA). All rights reserved.

The quiver Hopf algebras are classified by means of ramification system with irreducible representations. This leads to the classification of Nichols algebras over group algebras and pointed Nichols type Hopf algebras. 2000 Mathematics Subject Classification: 16W30, 16G10 keywords: Quiver, Hopf algebra, Hopf bimodule, Nichols algebras

We construct classes of von Neumann algebra modules by considering “column sums” of noncommutative Lp spaces. Our abstract characterization is based on an Lp/2-valued inner product, thereby generalizing Hilbert C*-modules and representations on Hilbert space. While the (single) representation theory is similar to the L2 case, the concept of Lp bimodule (p 6= 2) turns out to be nearly trivial.

We compute the Hochschild cohomology and homology of the algebra Λ = k〈x, y〉/(x2, xy + qyx, y2) with coefficients in 1Λψ for every degree preserving k-algebra automorphism ψ : Λ → Λ. As a result we obtain several interesting examples of the homological behavior of Λ as a bimodule.

Let A ⊂M be a MASA in a II1 factor M. We describe the von Neumann subalgebra of M generated by A and its normalizer N (A) as the set Nw q (A) consisting of those elements m ∈M for which the bimodule AmA is discrete. We prove that two MASAs A and B are conjugate by a unitary u ∈ Nw q (A) iff A is discrete over B and B is discrete over A in the sense defined by Feldman and Moore [5]. As a consequ...