Let $R$ be a 2-torsion free ring and $U$ be a square closed Lie ideal of $R$. Suppose that $alpha, beta$ are automorphisms of $R$. An additive mapping $delta: R longrightarrow R$ is said to be a Jordan left $(alpha,beta)$-derivation of $R$ if $delta(x^2)=alpha(x)delta(x)+beta(x)delta(x)$ holds for all $xin R$. In this paper it is established that if $R$ admits an additive mapping $G : Rlongrigh...

Let A be a factor von Neumann algebra with dimA ? 2. In this paper, it is proved that map : nonlinear mixed Jordan triple ?-derivation if and only an additive ?-derivation.

Let T (X) be the tensor bialgebra over an alphabet X. It is a graded connected cocommutative bialgebra, canonically isomorphic to the envelopping bialgebra of the free Lie algebra over X, Lie(X). The subalgebra of its convolution algebra generated by the projections arising from the graduation is also an algebra for the composition of morphisms and is anti-isomorphic as such with the direct sum...

We introduce a bicomplex which computes the triple cohomology of Lie– Rinehart algebras. We prove that the triple cohomology is isomorphic to the Rinehart cohomology [13] provided the Lie–Rinehart algebra is projective over the corresponding commutative algebra. As an application we construct a canonical class in the third dimensional cohomology corresponding to an associative algebra.

In commutative algebra, a Weitzenböck derivation is a nonzero triangular linear derivation of the polynomial algebra K[x1, . . . , xm] in several variables over a field K of characteristic 0. The classical theorem of Weitzenböck states that the algebra of constants is finitely generated. (This algebra coincides with the algebra of invariants of a single unipotent transformation.) In this paper ...

In this paper we provide an algebraic derivation of the explicit Witten volume formulas for a few semi-simple Lie algebras by combining a combinatorial method with the ideas used by Gunnells and Sczech in the computation of higher-dimensional Dedekind sums.