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 ...

We extend the notion of dually conjugate Hopf (super)algebras to the coloured Hopf (super)algebras Hc that we recently introduced. We show that if the standard Hopf (super)algebras Hq that are the building blocks of Hc have Hopf duals H∗ q , then the latter may be used to construct coloured Hopf duals Hc∗, endowed with coloured algebra and antipode maps, but with a standard coalgebraic structur...

It has long been known in universal algebra that any distributive sublattice of congruences of an algebra which consists entirely of commuting congruences yields a sheaf representation of the algebra. In this paper we provide a generalisation of this fact and prove a converse of the generalisation. To be precise, we exhibit a one-to-one correspondence (up to isomorphism) between soft sheaf repr...

One way to obtain Quantized Universal Enveloping Algebras (QUEAs) of non-semisimple Lie algebras is by contracting QUEAs of semisimple Lie algebras. We prove that every contracted QUEA in a certain class is a cochain twist of the corresponding undeformed universal envelope. Consequently, these contracted QUEAs possess a triangular quasi-Hopf algebra structure. As examples, we consider κ-Poincar...

In this paper we revisit and extend the constructions of Glauberman and Doro on groups with triality and Moufang loops to Hopf algebras. We prove that the universal enveloping algebra of any Lie algebra with triality is a Hopf algebra with triality. This allows us to give a new construction of the universal enveloping algebras of Malcev algebras. Our work relies on the approach of Grishkov and ...

Given a directed graph, there exists a universal operator algebra and universal C-algebra associated to the directed graph. In this paper we give intrinsic constructions of these objects. We provide an explicit construction for the maximal C-algebra of an operator algebra. We also discuss uniqueness of the universal algebras for finite graphs, showing that for finite graphs the graph is an isom...

We show that universal algebras with factorable congruences such as rings with 1 and semirings with 0 and 1 enjoy some of the properties of universal algebras whose congruence lattices are distributive, such as the strict refinement property and a variant of Jónsson’s lemma. A universal algebra A is said to have factorable congruences if whenever A ∼= B × C and θ is a congruence on A, then θ = ...

The basic purpose of the paper is to prepare preliminaries of the theory of many sorted algebras. The concept of the signature of a many sorted algebra is introduced as well as the concept of many sorted algebra itself. Some auxiliary related notions are defined. The correspondence between (1 sorted) universal algebras [8] and many sorted algebras with one sort only is described by introducing ...

We introduce the growth rank of a C∗-algebra — a (N∪ {∞})-valued invariant whose minimal instance is equivalent to the condition that an algebra absorbs the Jiang-Su algebra Z tensorially — and prove that its range is exhausted by simple, nuclear C∗-algebras. As consequences we obtain a well developed theory of dimension growth for approximately homogeneous (AH) C∗-algebras, establish the exist...

We obtain deformations of a crossed product of a polynomial algebra with a group, under some conditions, from universal deformation formulas. We show that the resulting deformations are nontrivial by a comparison with Hochschild cohomology. The universal deformation formulas arise from actions of Hopf algebras generated by automorphisms and skew derivations, and are universal in the sense that ...