Leibniz algebras are a non-anticommutative version of Lie algebras. They play an important role in different areas mathematics and physics have attracted much attention over the last thirty years. In this paper we investigate whether conditions such as being algebra, cyclic, simple, semisimple, solvable, supersolvable or nilpotent algebra preserved by lattice isomorphisms.

We shall discuss generic extension monoids associated with finite dimensional (basic) hereditary algebras of finite or cyclic type and related applications to Ringel–Hall algebras, (and hence, to quantum groups). We shall briefly review the geometric setting of quantum gln by Beilinson, Lusztig and MacPherson and its connections to Ringel– Hall algebras and q-Schur algebras. In the second part ...

We present some general techniques for constructing full-rank, minimal-delay, rate at least one space–time block codes (STBCs) over a variety of signal sets for arbitrary number of transmit antennas using commutative division algebras (field extensions) as well as using noncommutative division algebras of the rational field embedded in matrix rings. The first half of the paper deals with constr...

We prove that there exists a functorial correspondence between MV-algebras and partially cyclically ordered groups which are the wound-rounds of lattice-ordered groups. It follows some results about can be stated in terms MV-algebras. For example, study together with cyclic order allows to get first-order characterization unimodular complex numbers finite deduce pseudofinite MV-chains pseudo-si...

We define and study equivariant analytic and local cyclic homology for smooth actions of totally disconnected groups on bornological algebras. Our approach contains equivariant entire cyclic cohomology in the sense of Klimek, Kondracki and Lesniewski as a special case and provides an equivariant extension of the local cyclic theory developped by Puschnigg. As a main result we construct a multip...

We introduce an equivariant version of cyclic cohomology for Hopf module algebras. For any H-module algebra A, where H is a Hopf algebra with S2 = idH we define the cocyclic module C ♮ H(A) and we find its relation with cyclic cohomology of crossed product algebra A ⋊ H. We define K 0 (A), the equivariant K-theory group of A, and its pairing with cyclic and periodic cyclic cohomology of C H(A).

This paper builds a general framework in which to study cohomology theories of strongly homotopy algebras, namely A∞, C∞ and L∞-algebras. This framework is based on noncommutative geometry as expounded by Connes and Kontsevich. The developed machinery is then used to establish a general form of Hodge decomposition of Hochschild and cyclic cohomology of C∞-algebras. This generalizes and puts in ...

We study the classification of group actions on C*-algebras up to equivariant KK-equivalence. show that any action is equivariantly KK-equivalent an a simple, purely infinite C*-algebra. conjecture Izumi equivalent equivalence between cocycle conjugacy and KK-equivalence for torsion-free amenable groups Kirchberg algebras. Let G be cyclic prime order. describe its KK-equivalence, based previous...

Cλ-extended oscillator algebras, where Cλ is the cyclic group of order λ, are introduced and realized as generalized deformed oscillator algebras. For λ = 2, they reduce to the well-known Calogero–Vasiliev algebra. For higher λ values, they are shown to provide in their bosonic Fock space representation some interesting applications to supersymmetric quantum mechanics and some variants thereof:...