In this paper we investigate the structure and representation of n-ary algebras arising from DNA recombination, where n is a number of DNA segments participating in recombination. Our methods involve a generalization of the Jordan formalization of observables in quantum mechanics in n-ary splicing algebras. We show that the splicing algebras are an n-ary envelope for algebras of DNA recombinati...

It is proved that classifiable simple separable nuclear purely infinite C∗algebras having finitely generated K-theory and torsion-free K1 are semiprojective. This is accomplished by exhibiting these algebras as C∗-algebras of infinite directed graphs.

We review some applications of Gröbner-Shirshov bases, including PBW theorems, linear bases of free universal algebras, normal forms for groups and semigroups, extensions of groups and algebras, embedding of algebras.

In this paper, we first define the pre-Lie family algebra associated to a dendriform in case of commutative semigroup. Then construct via typed decorated rooted trees, and prove freeness algebra. We also operad terms labeled obtain that algebras is isomorphic which generalizes result Chapoton Livernet. end, Zinbiel pre-Poisson generalize results Aguiar.

we study topological von neumann regularity and principal von neumann regularity of banach algebras. our main objective is comparing these two types of banach algebras and some other known banach algebras with one another. in particular, we show that the class of topologically von neumann regular banach algebras contains all $c^*$-algebras, group algebras of compact abelian groups and cer...

In this lecture we discuss ‘beyond CFT’ from symmetry point of view. After reviewing the Virasoro algebra, we introduce deformed Virasoro algebras and elliptic algebras. These algebras appear in solvable lattice models and we study them by free field approach.

Non-commutative Hilbert schemes, introduced by M. V. Nori, parametrize left ideals of finite codimension in free algebras. More generally, parameter spaces of finite codimensional submodules of free modules over free algebras are considered. Cell decompositions of these varieties are constructed, whose cells are parametrized by certain types of forests. Properties of the corresponding generatin...

Abstract. We use free probability techniques to compute borders of spectra of non hermitian operators in finite von Neumann algebras which arise as “free sums” of “simple” operators. To this end, the resolvent is analyzed with the aid of the Haagerup inequality. Concrete examples coming from reduced C∗-algebras of free product groups and leading to systems of polynomial equations illustrate the...

Let E be a set of inequalities between finite Σ-terms. Let Vω and Vr denote the varieties of all ω-continuous ordered Σ-algebras and regular ordered Σ-algebras satisfying E, respectively. We prove that the free Vr-algebra R(X) on generators X is the subalgebra of the corresponding free Vω-algebra Fω(X) determined by those elements of Fω(X) denoted by the regular Σ-coterms. We actually establish...