Abstract. The underlying field is of characteristic p > 2. In this paper, we first use the method of computing the homogeneous derivations to determine the first cohomology of the so-called odd contact Lie algebra with coefficients in the even part of the generalized Witt Lie superalgebra. In particular, we give a generating set for the Lie algebra under consideration. Finally, as an applicatio...

Throughout this note, R will be always a prime ring of characteristic different from 2 with center Z(R), extended centroid C, and two-sided Martindale quotient ring Q. Let f : R→ R be additive mapping of R into itself. It is said to be a derivation of R if f (xy)= f (x)y + x f (y), for all x, y ∈ R. Let S⊆ R be any subset of R. If for any x, y ∈ S, f ([x, y])= [ f (x), y] + [x, f (y)], then the...

We introduce a dual notion of the Poisson algebra, called transposed by exchanging roles two binary operations in Leibniz rule defining algebra. The algebra shares common properties and arises naturally from Novikov-Poisson taking commutator Lie Novikov Consequently, classic construction commutative with commuting derivations similarly applies to More broadly, captures algebraic structures when...

In this paper, we study universal central extensions and non-abelian tensor product of hom-Lie–Rinehart algebras. We discuss $\alpha $-central extensions, the lifting automorphisms $-derivations to hom-Li

We introduce Courant 1-derivations, which describe a compatibility between algebroids and linear (1,1)-tensor fields lead to the notion of Courant-Nijenhuis algebroids. provide examples 1-derivations on exact show that holomorphic can be viewed as special types By considering Dirac structures, one recovers Dirac-Nijenhuis structures previously studied by authors (in case standard algebroid) obt...