We show that pseudovarieties of finitely generated algebras, i.e., classes C of finitely generated algebras closed under finite products, homomorphic images, and subalgebras, can be described via a uniform structure UC on the free algebra for C: the members of C then are precisely those finitely generated algebras A for which the natural mapping from the free algebra onto the term clone of A is...

Last years a number of papers were devoted to describing automorphisms of semigroups of endomorphisms of free finitely generated universal algebras of some varieties: groups, semigroups, associative commutative algebras, inverse semigroups, modules, Lie algebras and some others (see references). All these researches were inspired by the questions prof. B. Plotkin set in connection with so calle...

Leivant’s ramified recurrence is one of the earliest examples of an implicit characterization of the polytime functions as a subalgebra of the primitive recursive functions. Leivant’s result, however, is originally stated and proved only for word algebras, i.e. free algebras whose constructors take at most one argument. This paper presents an extension of these results to ramified functions on ...

Parallel to the first two authors’ earlier classification of separable unital oneparameter continuous fields of Kirchberg algebras with torsion free K-groups supported in one dimension, one-parameter separable unital continuous fields of AF-algebras are classified by their ordered K0-sheaves. We prove Effros-Handelman-Shen type theorems for separable unital one-parameter continuous fields of AF...

The study of free Baxter algebras was started by Rota and Cartier thirty years ago. We continue this study by applying two recent constructions of free Baxter algebras. We investigate the basic structure of a free Baxter algebra, and characterize in detail when a free Baxter algebra is a domain or a reduced algebra. We also describe the nilpotent radical of a free Baxter algebra when it is not ...

By generalizing the Miura transformation for WN to other classical W algebras obtained by hamiltonian reduction, we find realisations of these algebras in terms of relatively simple non-abelian current algebras, e.g. ŝl(2) × û(1)N , generalizing the free field realisation of WN . As an example, we present the ŝl(2)× û(1) realisation of W2 3 , which we also quantize. By a specific example, we al...

Given a directed graph, there exists a universal operator algebra and universal C∗-algebra associated to the directed graph. For finite graphs this algebra decomposes as the universal free product of some building block operator algebras. For countable directed graphs, the universal operator algebras arise as direct limits of operator algebras of finite subgraphs. Finally, a method for computin...

Parametrized iterativity of an algebra means the existence of unique solutions of all finitary recursive systems of equations where recursion is allowed to use only some variables (chosen as a parameter). We show how such algebras can be introduced in an arbitrary category A by employing a base, i.e., an operation interpreting objects of A as monads on A. For every base we prove that free base ...

since 2005 a new powerful invariant of an algebra has emerged using the earlier work of horvath, hethelyi, kulshammer and murray. the authors studied morita invariance of a sequence of ideals of the center of a nite dimensional algebra over a eld of nite characteristic. it was shown that the sequence of ideals is actually a derived invariant, and most recently a slightly modied version o...

An algebra A is uniquely generated by a set G if G is a subset of every set that generates A. We investigate uniquely generated algebras and focus especially on equational classes of algebras in which the free algebras are uniquely generated. We show that such classes possess a number of algebraic properties that are in some sense extremal. We also present algebraic conditions on an equational ...