Lazard showed in his seminal work [L] that for rational coefficients continuous group cohomology of p-adic Lie-groups is isomorphic to Lie-algebra cohomology. We refine this result in two directions: firstly we extend his isomorphism under certain conditions to integral coefficients and secondly, we show that for algebraic groups, his isomorphism can be realized by differentiating locally analy...

In this paper, first we introduce the notion of a twisted Rota-Baxter operator on 3-Lie algebra $\g$ with representation $V$. We show that induces structure $V$, which represents $\g$. By fact, define cohomology and study infinitesimal deformations using second group. Then an NS-3-Lie algebra, produces itself. naturally. Thus algebras can be viewed as underlying algebraic structures operators a...

0. Introduction. 1. Let G be a group of linear transformations on a finite dimensional real or complex vector space X. Assume X is completely reducible as a G-module. Let 5 be the ring of all complexvalued polynomials on X, regarded as a G-module in the obvious way, and let J C 5 be the subring of all G-invariant polynomials on X. Now let J be the set of all ƒ £ J having zero constant term and ...

We study the homological properties of the factor space G/P, where G is a complex semisimple Lie group and Ρ a parabolic subgroup of G. To this end we compare two descriptions of the cohomology of such spaces. One of these makes use of the partition of G/P into cells (Schubert cells), while the other consists in identifying the cohomology of G/P with certain polynomials on the Lie algebra of th...

Let G be an exceptional Lie group with a maximal torus T ⊂ G. We express the integral cohomology ring H(G/T ) by a minimal set of Schubert classes on G/T . This completes the program of determining the integral cohomology of all complete flag manifolds G/T in the context of Schubert calculus. The results are used in [DZ3] to construct the integral cohomology of a simple Lie group G in terms of ...