in this paper, we classify the indecomposable non-nilpotent solvable lie algebras with $n(r_n,m,r)$ nilradical,by using the derivation algebra and the automorphism group of $n(r_n,m,r)$.we also prove that these solvable lie algebras are complete and unique, up to isomorphism.

let $n$ be a submodule of a module $m$ and a minimal primary decomposition of $n$ is known‎. ‎a formula to compute baer's lower nilradical of $n$ is given‎. ‎the relations between classical prime submodules and their nilradicals are investigated‎. ‎some situations in which semiprime submodules can be written as finite intersection of classical prime submodule are stated‎.

We study disemisimple Lie algebras, i.e., algebras which can be written as a vector space sum of two semisimple subalgebras. show that algebra g is if and only its solvable radical coincides with nilradical prehomogeneous s-module for Levi subalgebra s g. use the classification s-modules simple given by Vinberg to abelian. extend this result having no quotients type A.

The Lichnerowicz conjecture asserted that every harmonic Riemannian manifold is locally isometric to a two-point homogeneous space. In 1992, E. Damek and F. Ricci produced a family of counter-examples to this conjecture, which arise as abelian extensions of two-step nilpotent groups of type-H. In this paper we consider a broader class of Riemannian manifolds: solvmanifolds of Iwasawa type with ...

This paper begins a series studying D-modules on the Feigin-Frenkel semi-infinite flag variety from the perspective of the Beilinson-Drinfeld factorization (or chiral) theory. Here we calculate Whittaker-twisted cohomology groups of Zastava spaces, which are certain finite-dimensional subvarieties of the affine Grassmannian. We show that such cohomology groups realize the nilradical of a Borel ...

In this work, we consider extensions of solvable Lie algebras with naturally graded filiform nilradicals. Note that there exist two [Formula: see text] and We find all one-dimensional nilradical text]. prove exists a unique non-split central extension maximal codimension. Moreover, whose codimension is equal to one are found compared these the nilradicals algebra

Let L be a Lie pseudoalgebra, a ∈ L. We show that, if a generates a (finite) solvable subalgebra S = 〈a〉 ⊂ L, then one may find a lifting ā ∈ S of [a] ∈ S/S such that 〈ā〉 is nilpotent. We then apply this result towards vertex algebras: we show that every finite vertex algebra V admits a decomposition into a semi-direct product V = U⋉N , where U is a subalgebra of V whose underlying Lie conforma...

The volume of a line bundle is defined in terms limsup. It fundamental question whether this limsup limit. has been shown that always the case on generically reduced schemes. We show volumes are limits two classes schemes not necessarily reduced: codimension one subschemes projective varieties such their components maximal dimension contain normal points and whose nilradical squared equals zero.