Curvature in Nilpotent Lie Groups
نویسندگان
چکیده
Colloq. Algebraic Topology, 1962, pp. 104-113, Matematisk Institut, Aarhus Universitet, Denmark. 4. M. F. Atiyah, Thorn complexes, Proc. London Math. Soc. (3) 11 (1961), 291310. 5. M. F. Atiyah and J. A. Todd, On complex Stiefel manifolds, Proc. Cambridge Philos. Soc. 56 (1960), 342-353. 6. Sze-Tsen Hu, Homotopy theory, Pure and Applied Mathematics VIII, Academic Press, New York and London, 1959. 7. I. M. James, Spaces associated with Stiefel manifolds, Proc. London Math. Soc. (3)9(1959), 115-140.
منابع مشابه
Some properties of nilpotent Lie algebras
In this article, using the definitions of central series and nilpotency in the Lie algebras, we give some results similar to the works of Hulse and Lennox in 1976 and Hekster in 1986. Finally we will prove that every non trivial ideal of a nilpotent Lie algebra nontrivially intersects with the centre of Lie algebra, which is similar to Philip Hall's result in the group theory.
متن کاملThe structure of a pair of nilpotent Lie algebras
Assume that $(N,L)$, is a pair of finite dimensional nilpotent Lie algebras, in which $L$ is non-abelian and $N$ is an ideal in $L$ and also $mathcal{M}(N,L)$ is the Schur multiplier of the pair $(N,L)$. Motivated by characterization of the pairs $(N,L)$ of finite dimensional nilpotent Lie algebras by their Schur multipliers (Arabyani, et al. 2014) we prove some properties of a pair of nilpoten...
متن کاملOn dimension of a special subalgebra of derivations of nilpotent Lie algebras
Let $L$ be a Lie algebra, $mathrm{Der}(L)$ be the set of all derivations of $L$ and $mathrm{Der}_c(L)$ denote the set of all derivations $alphainmathrm{Der}(L)$ for which $alpha(x)in [x,L]:={[x,y]vert yin L}$ for all $xin L$. We obtain an upper bound for dimension of $mathrm{Der}_c(L)$ of the finite dimensional nilpotent Lie algebra $L$ over algebraically closed fields. Also, we classi...
متن کاملSolvable Lie algebras with $N(R_n,m,r)$ nilradical
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.
متن کاملACTION OF SEMISIMPLE ISOMERY GROUPS ON SOME RIEMANNIAN MANIFOLDS OF NONPOSITIVE CURVATURE
A manifold with a smooth action of a Lie group G is called G-manifold. In this paper we consider a complete Riemannian manifold M with the action of a closed and connected Lie subgroup G of the isometries. The dimension of the orbit space is called the cohomogeneity of the action. Manifolds having actions of cohomogeneity zero are called homogeneous. A classic theorem about Riemannian manifolds...
متن کاملBounds for the dimension of the $c$-nilpotent multiplier of a pair of Lie algebras
In this paper, we study the Neumann boundary value problem of a class of nonlinear divergence type diffusion equations. By a priori estimates, difference and variation techniques, we establish the existence and uniqueness of weak solutions of this problem.
متن کامل