This is the final one in the series of papers where we introduce and study the C∗-algebras associated with topological graphs. In this paper, we get a sufficient condition on topological graphs so that the associated C∗-algebras are simple and purely infinite. Using this result, we give one method to construct all Kirchberg algebras as C∗-algebras associated with topological graphs. 0. Introduc...

It is well known that any Lie algebra can be embedded into an associative algebra. We prove metabelian in the subvariety of perm algebras, i.e. algebras with identity [Formula: see text]. In addition, a technical method to construct universal enveloping for given.

This paper is a contribution to the isomorphism problem for universal enveloping algebras of finite-dimensional Lie algebras. We focus on solvable small dimensions over fields arbitrary characteristic. prove, an field, that type metabelian algebra whose derived subalgebra has codimension one determined by its algebra. As application results in this paper, we solve dimension four characteristic ...

Prof. Boris I. Plotkin [1, 2] drew attention to the question when an equivalence between two categories is isomorphic as a functor to an isomorphism between them. It turns out that it is quite important for universal algebraical geometry and concerns mainly the categories Θ0(X) of free universal algebras of some variety Θ free generated by finite subsets of X. In the paper, a complete answer to...

We prove that a number of classes of separable unital C*-algebras are closed under crossed products by finite group actions with the Rokhlin property, including: • AI algebras, AT algebras, and related classes characterized by direct limit decompositions using semiprojective building blocks. • Simple unital AH algebras with slow dimension growth and real rank zero. • C*-algebras with real rank ...

Every computable universal algebra has a finitely presented expansion, but there are examples of finitely generated, computably enumerable universal algebras with no finitely presented expansions. It is natural to ask whether such examples can be found in well-known classes of algebras such as groups and semigroups. In this paper, we build an example of a finitely generated, infinite, computabl...

We explicitly compute the first and second cohomology groups of the classical Lie superalgebras slm|n and osp2|2n with coefficients in the finite dimensional irreducible modules and the Kac modules. We also show that the second cohomology groups of these Lie superalgebras with coefficients in the respective universal enveloping algebras (under the adjoint action) vanish. The latter result in pa...

Studying Jone’s polynomials in node theories, their generalization and their connections with ”vertex models” in two-dimensional statistical mechanics, Witten presents Hoph algebra deformations of the universal enveloping algebra su(2). There is a family of associative algebras depending on a real parameter p. These algebras are given by the generators E0, E+, E− and relations [2]: pE0E+ − 1 p ...