Related papers: Villadsen algebras are singly generated

There are 10 generalized Kac-Moody algebras whose denominator identities are completely reflective automorphic products of singular weight on lattices of squarefree level. Under the assumption that the meromorphic vertex operator algebra of…

We will show that separable unital AF-algebras whose Bratteli diagrams do not allow converging two nodes into one node, can be classified up to the tensor product with the universal UHF-algebra $\Q$ only by their trace spaces. That is, if…

A separating algebra is, roughly speaking, a subalgebra of the ring of invariants whose elements distinguish between any two orbits that can be distinguished using invariants. In this paper, we introduce a geometric notion of separating…

This paper gives an analogue of A_g(V) theory for a vertex operator superalgebra V and an automorphism g of finite order. The relation between the g-twisted V-modules and A_g(V)-modules is established. It is proved that if V is g-rational,…

We introduce a subclass of recursive subhomogeneous algebras, in which each of the pullback maps is diagonal in a suitable sense. We define the notion of a diagonal map between two such algebras and show that every simple inductive limit of…

It is shown that the *-algebra of all (closed densely defined linear) operators affiliated with a finite type I von Neumann algebra admits a unique center-valued trace, which turns out to be, in a sense, normal. It is also demonstrated that…

Numerical characteristics of identities of finite-dimensional nonassociative algebras are studied. The main result is the construction of a four-dimensional simple unitary algebra with fractional PI-exponent strictly less than its…

It is proved that for any natural number $n$ the subalgebra of a free finitely generated alternative algebra generated by all the words on generators whose length is a multiple of $n$ (the Veronese $n$-subalgebra), is finitely generated.

A novel generalization of the Askey-Wilson algebra is presented and shown to be associated with coproducts in the quantum algebra $U_q(su(1,1))$. This algebra has 15 non-commuting generators given by $Q^{(A)}$, with $A\subset \{1,2,3,4\}$…

Say that a separable, unital C*-algebra D is strongly self-absorbing if there exists an isomorphism $\phi: D \to D \otimes D$ such that $\phi$ and $id_D \otimes 1_D$ are approximately unitarily equivalent $*$-homomorphisms. We study this…

The Grigorchuk and Gupta-Sidki groups play fundamental role in modern group theory. Their natural analogues are self-similar nil Lie $p$-algebras. In characteristic zero, similar examples of Lie algebras do not exist (Martinez and…

Over a field $F$ of any characteristic, for a commutative associative algebra $A$ with an identity element and for the polynomial algebra $F[D]$ of a commutative derivation subalgebra $D$ of $A$, the associative and the Lie algebras of Weyl…

We study the class of simple C*-algebras introduced by Villadsen in his pioneering work on perforated ordered K-theory. We establish six equivalent characterisations of the proper subclass which satisfies the strong form of Elliott's…

An algebra $A$ is said to be directly finite if each left invertible element in the (conditional) unitization of $A$ is right invertible. We show that the reduced group ${\rm C}^\ast$-algebra of a unimodular group is directly finite,…

A new class of nonassociative algebras, Vidinli algebras, is defined based on recent work of Co\c{s}kun and Eden. These algebras are conic (or quadratic) algebras with the extra restriction that the commutator of any two elements is a…

Axial algebras are a class of commutative non-associative algebras which have a natural group of automorphisms, called the Miyamoto group. The motivating example is the Griess algebra which has the Monster sporadic simple group as its…

We prove a uniqueness theorem and give a characterization of simplicity for Steinberg algebras associated to non-Hausdorff ample groupoids. We also prove a uniqueness theorem and give a characterization of simplicity for the C*-algebra…

In this article, we prove $K$-stability for a family of $C^*$-algebras, which are generated by a finite set of unitaries and isometries satisfying twisted commutation relations. This family includes the $C^*$-algebra of doubly non-commuting…

Supersymmetry and super-Lie algebras have been consistently generalized previously. The so-called fractional supersymmetry and $F-$Lie algebras could be constructed starting from any representation $\D$ of any Lie algebra $g$. This involves…

Classification, up to isomorphism, of algebras from a non-empty subset of the variety of $n$- dimensional algebras is presented. It is shown that these algebras have only trivial automorphism and if the basic field is algebraically closed…