On a manifold with a projective connection we canonically assign a second order differential operator acting on the algebra of all densities to any tensor density S of fixed weight λ. In particular, this implies that on any projectively connected manifold, a ‘bracket’ (symmetric biderivation) on the algebra of functions extends canonically to the algebra of densities.

Bresar in 1993 proved that each biderivation on a noncommutative prime ring is a multiple of a commutatot. A result of it is a characterization of commuting additive mappings, because each commuting additive map give rise to a biderivation. Then in 1995, he investigated biderivations, generalized biderivations and sigma-biderivations on a prime ring and generalized the results of derivations fo...

Let W be a simple generalized Witt algebras over a field of characteristic zero. In this paper, it is proved that each anti-symmetric biderivation of W is inner. As an application of biderivations, it is shown that a linear map ψ on W is commuting if and only if ψ is a scalar multiplication map on W. The commuting automorphisms and derivations of W are determined.

We study conformal biderivations of a Lie algebra. First, we give the definition biderivation. Next, determine loop W(a, b) algebra, Virasoro and Especially, all on algebra are inner biderivations.

Motivated by the Poisson Dixmier-Moeglin equivalence problem, a systematic study of commutative unitary rings equipped with biderivation, namely binary operation that is derivation in each argument, here begun, an eye toward geometry corresponding B-varieties. Foundational results about extending biderivations to localisations, algebraic extensions and transcendental are established. Resolving ...

There are also four appendices. Let K be a field of characteristic 0, and let C be a commutative K-algebra. which makes C into a Lie algebra, and is a biderivation (i.e. a derivation in each argument). The pair C, {−, −} is called a Poisson algebra. Poisson brackets arise in several ways. Example 1.1. Classical Hamiltonian mechanics. Here K = R, X is an even dimensional differentiable manifold ...