We compare the K-theory and K-homology of the well known CAR algebra. While the K0 group is infinitely generated, we show that it pairs identically to zero with even Fredholm modules over the algebra. We show further that in fact the even K-homology is trivial, while the odd K-homology group is very large. These results give some insight into the K-homology of AF-algebras. 1. The CAR algebra We...

We describe the Kantor square (and product) of multiplications, extending classification proposed in [I. Kaygorodov, On product, Journal Algebra and Its Applications, 16 (2017), 9, 1750167]. Besides, we explicitly some low dimensional algebras give constructive methods for obtaining new transposed Poisson Poisson-Novikov algebras; classifying structures commutative post-Lie on a given algebra.

We provide more characterizations of varieties having a term Mal’cev modulo two functions F and G. We characterize varieties neutral in the sense of F , that is varieties satisfying R ⊆ F (R). We present examples of global operators satisfying the homomorphism property, in particular we show that many known commutators satisfy the homomorphism property. See Parts I-III [2] for unexplained notat...

We introduce a notion of secondary characteristic classes of Lie algebra extensions. As a spin-off of our construction we obtain a new proof of Lecomte’s generalization of the Chern–Weil homomorphism.

We define the Lukasiewicz transform as a residuated map and a homomorphism between semimodules over the semiring reducts of an MV-algebra. Then we describe the “ Lukasiewicz Transform Based” ( LTB) algorithm for image processing, demonstrating its applicability.

In this paper, we prove Hyers-Ulam-Rassias stability of $C^*$-ternary algebra homomorphism for the following generalized Cauchy-Jensen equation $$eta mu fleft(frac{x+y}{eta}+zright) = f(mu x) + f(mu y) +eta f(mu z)$$ for all $mu in mathbb{S}:= { lambda in mathbb{C} : |lambda | =1}$ and for any fixed positive integer $eta geq 2$ on $C^*$-ternary algebras by using fixed poind alternat...

We find the universal module w(M) for functions (that need not be invariants) of finite matroids, defined on a minor-closed class M and with values in any module L over any commutative and unitary ring, that satisfy a parametrized deletion-contraction identity, F (M) = δeF (M r e) + γeF (M/e), when e is neither a loop nor a coloop. (F is called a (parametrized) weak Tutte function.) Within the ...

Poisson algebras are usually defined as structures with two operations, a commutative associative one and an anticommutative one satisfying the Jacobi identity. These operations are tied up by a distributive law, the Leibniz law. We present Poisson algebras as algebras with one operation which enables one to study them as part of nonassociative algebras. We study the algebraic and cohomological...

Let $W = \mathbb {C}[t,t^{-1}]\partial _t$ be the Witt algebra of algebraic vector fields on $\mathbb {C}^\times$ and let $V\!ir$ Virasoro , unique nontrivial central extension $W$ . In this paper, we study Poisson ideal structure symmetric algebras as well several related Lie algebras. We classify prime ideals primitive $\operatorname {S}(V\!ir)$ {S}(W)$ particular, show that only functions in...