We analyze in the context of Leavitt path algebras some graph operations introduced in the context of symbolic dynamics by Williams, Parry and Sullivan, and Franks. We show that these operations induce Morita equivalence of the corresponding Leavitt path algebras. As a consequence we obtain our two main results: the first gives sufficient conditions for which the Leavitt path algebras in a cert...

We describe the isomorphism classes of infinite-dimensional graded Lie algebras of maximal class over fields of odd characteristic.

We present a list of all isomorphism classes of nonsolvable Lie algebras of dimension ≤ 6 over a finite field.

In present work we consider C∗-algebras C∗(Af ) associated with simple unimodal nonbijective dynamical system (f,R) with special requirements. In the case when f is polynomial, Af = C〈X,X∗| XX∗ = f(X∗X)〉 and C∗(Af ) is its enveloping C∗-algebra. As typical examples we consider one-parameter family fμ(x) = μx(1 − x) and two-parameter family called Unharmonic Quantum Oscillator fp,q(x) = 1+ px− q...

A category is described to which the Cuntz semigroup belongs and as a functor into which it preserves inductive limits. 1. Recently, Toms in [26] used the refinement of the invariant K0 introduced by Cuntz almost thirty years ago in [4] to show that certain C*-algebras are not isomorphic. Anticipating the possible use of this invariant to establish isomorphism, we take the liberty of reporting ...

Clifford algebras are naturally associated with quadratic forms. These algebras are Z2 -graded by construction. However, only a Zn -gradation induced by a choice of a basis, or even better, by a Chevalley vector space isomorphism Cl(V ) ↔ ∧ V and an ordering, guarantees a multivector decomposition into scalars, vectors, tensors, and so on, mandatory in physics. We show that the Chevalley isomor...

In this paper we prove a conjecture of B. Shoikhet. This conjecture states that the tangent isomorphism on homology, between the Poisson homology associated to a Poisson structure on R d and the Hochschild homology of its quantized star-product algebra , is an isomorphism of modules over the (isomorphic) respective cohomology algebras. As a consequence, we obtain a version of the Duflo isomorph...

In this work we approach three-dimensional evolution algebras from certain constructions performed on two-dimensional algebras. More precisely, provide four different producing Also introduce two parameters, the annihilator stabilizing index and socle index, which are useful tools in classification theory of these Finally, use moduli sets as a convenient way to describe isomorphism classes