Abstract We study locally conformally balanced metrics on almost abelian Lie algebras, namely solvable algebras admitting an ideal of codimension one, providing characterizations in every dimension. Moreover, we classify six-dimensional and some compatibility results between different types special Hermitian groups their compact quotients. end by classifying hyperkähler structures.

In this paper we describe the derivations of orthosymplectic Lie superalgebras over a superring. In particular, we derive sufficient conditions under which the derivations can be expressed as a semidirect product of inner and outer derivations. We then present some examples for which these conditions hold.

We consider the natural Lie algebra structure on the (associative) group algebra of a finite group G, and show that the Lie subalgebras associated to natural involutive antiautomorphisms of this group algebra are reductive ones. We give a decomposition in simple factors of these Lie algebras, in terms of the ordinary representations of G. MSC 2000 : 20C15,17B99.

A well known theorem of Duflo, the “annihilation theorem”, claims that the annihilator of a Verma module in the enveloping algebra of a complex semisimple Lie algebra is centrally generated. For the Lie superalgebra osp(1, 2l), this result does not hold. In this article, we introduce a “correct” analogue of the centre for which the annihilation theorem does hold in the case osp(1, 2l). This sub...

A subalgebra B of a Leibniz algebra L is called weak c-ideal if there subideal C such that L=B+C and B∩C⊆BL where BL the largest ideal contained in B. This analogous to concept weakly c-normal subgroup, which has been studied by number authors. We obtain some properties c-ideals use them give characterizations solvable supersolvable algebras generalizing previous results for Lie algebras. note ...

In this paper we explicitly determine the derivation algebra, automorphism group of quasi Qn-filiform Lie algebras, and applying some properties of root vector decomposition we obtain their isomorphism theorem. AMS Classification: 17B05; 17B30

‎in this paper, we formulate the fourth order sturm-liouville problem (fslp) as a lie group matrix differential equation. by solving this ma- trix differential equation by lie group magnus expansion, we compute the eigenvalues of the fslp. the magnus expansion is an infinite series of multiple integrals of lie brackets. the approximation is, in fact, the truncation of magnus expansion and a gauss...

We attach a Dixmier algebra B to the closure O of any nilpotent orbit of G where G is GL(n, C), O(n, C) or Sp(2n, C). This algebra B is a noncommutative analog of the coordinate ring R of O, in the sense that B has a G-invariant algebra filtration and grB = R. We obtain B by making a noncommutative analog of the Kraft-Procesi construction which modeled O as the algebraic symplectic reduction of...

These notes are an introduction to Lie algebras, algebraic groups, and Lie groups in characteristic zero, emphasizing the relationships between these objects visible in their categories of representations. Eventually these notes will consist of three chapters, each about 100 pages long, and a short appendix. Single paper copies for noncommercial personal use may be made without explicit permiss...