We obtain deformations of a crossed product of a polynomial algebra with a group, under some conditions, from universal deformation formulas. These formulas arise from actions of Hopf algebras generated by automorphisms and skew derivations. They are universal in the sense that they apply to deform all algebras with such Hopf algebra actions, and we give one additional example.

This article describes the algebraic approach to Constraint Satisfaction Problem that led to many developments in both CSP and universal algebra. No prior knowledge of universal algebra is assumed. 1998 ACM Subject Classification F.2.0 [Analysis of Algorithms and Problem Complexity] General, F.2.0 [Discrete Mathematics] General

In this paper we study the algebra L(Σ) generated by links in the manifold Σ¬[0, 1] where Σ is an oriented surface. This algebra has a filtration and the associated graded algebra L Gr (Σ) is naturally a Poisson algebra. There is a Poisson algebra homomorphism from the algebra ch (Σ) of chord diagrams on Σ to L Gr (Σ). We show that multiplication in L (Σ) provides a geometric way to define a de...

We find a self-dual noncommutative and noncocommutative Hopf algebra HF acting as a universal symmetry on the modules over inner Frobenius algebras of modular categories (as used in two dimensional boundary conformal field theory) similar to the GrothendieckTeichmüller groupGT as introduced by Drinfeld as a universal symmetry of quasitriangular quasi-Hopf algebras. We discuss the relationship t...

A covering of k-graphs (in the sense of Pask-Quigg-Raeburn) induces an embedding of universal C∗-algebras. We show how to build a (k + 1)-graph whose universal algebra encodes this embedding. More generally we show how to realise a direct limit of k-graph algebras under embeddings induced from coverings as the universal algebra of a (k + 1)-graph. Our main focus is on computing the K-theory of ...

Anick proved that every q-mild Hopf algebra up to homotopy is isomorphic to the universal enveloping algebra of a chain Lie algebra. We provide a new proof, that involves extensive use of the Bockstein spectral sequence.

We identify the symmetry algebra of the Laplacian on Euclidean space as an explicit quotient of the universal enveloping algebra of the Lie algebra of conformal motions. We construct analogues of these symmetries on a general conformal manifold.