A thin Lie algebra is a Lie algebra graded over the positive integers satisfying a certain narrowness condition. We describe several cyclic grading of the modular Hamiltonian Lie algebras H(2 : n;ω2) (of dimension one less than a power of p) from which we construct infinite-dimensional thin Lie algebras. In the process we provide an explicit identification of H(2 : n;ω2) with a Block algebra. W...

We introduce Lie-Nijenhuis bialgebroids as Lie endowed with an additional derivation-like object. They give a complete infinitesimal description of Poisson-Nijenhuis groupoids, and key examples include manifolds, holomorphic flat bialgebra bundles. To achieve our goal we develop theory "generalized derivations" their duality, extending the well-established derivations on vector

We prove nilpotency results for Lie algebras over an arbitrary field admitting a derivation, which satisfies given polynomial identity r(t) = 0. In the special case of r=tn−1 we obtain uniform bound on class periodic derivation order n. even find optimal in characteristic p if does not divide certain invariant ρn.

In this paper we study the Lie algebras of derivations two-step nilpotent algebras. We obtain a class with trivial center and abelian ideal inner derivations. Among these, relations between complex real case indecomposable Heisenberg Leibniz are thoroughly described. Finally show that every almost derivation algebra one-dimensional commutator ideal, three exceptions, is an derivation.

We prove that the automorphisms of the generalized Witt Lie algebras W(m , n) over arbitrary commutative rings of characteristic p > 3 all come from automorphisms of the algebras on which they are defined as derivations. By descent theory, this result then implies that if a Lie algebra over a field becomes isomorphic to W{m, n) over the algebraic closure, it is a derivation algebra of the type ...

In the present paper, we study simple algebras, which do not belong to well-known classes of algebras (associative alternative Lie Jordan etc.). The finite-dimensional over a field characteristic 0 without finite basis identities, constructed by Kislitsin, are such algebras. consider two algebras: seven-dimensional anticommutative algebra \(\mathcal{D}\) and central commutative \(\mathcal{C}\)....