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...

Let M be a compact surface with (M) < 0 and let G be a compact Lie group whose Levi factor is a product of groups locally isomorphic to SU(2) (for example SU(2)). Then the map

We develop a machinery which translates results on algebraic sums of sets of reals into the corresponding results on their cartesian product. Some consequences are: (1) The product of meager/null-additive sets in the Cantor space is meager/nulladditive, respectively. (2) The product of a meager/null-additive set and a strong measure zero/strongly meager set in the Cantor space has strong measur...

It is shown, that each Lifting cocycle Ψ2n+1,Ψ2n+3,Ψ2n+5, . . . ([Sh1], [Sh2]) on the Lie algebra Difn of polynomial differential operators on an n-dimensional complex vector space is the sum of two cocycles, its even and odd part. We study in more details the first case n = 1. It is shown, that any nontrivial linear combination of two 3-cocycles on the Lie algebra Dif1, arising from the 3-cocy...

let $mathcal{a}$ and $mathcal{b}$ be two $c^{*}$-algebras such that $mathcal{b}$ is prime. in this paper, we investigate the additivity of maps $phi$ from $mathcal{a}$ onto $mathcal{b}$ that are bijective, unital and satisfy $phi(ap+eta pa^{*})=phi(a)phi(p)+eta phi(p)phi(a)^{*},$ for all $ainmathcal{a}$ and $pin{p_{1},i_{mathcal{a}}-p_{1}}$ where $p_{1}$ is a nontrivial projection in $mathcal{a...

A generalization of the Jordan–Schwinger map: classical version and its q–deformation. Abstract For all three–dimensional Lie algebras the construction of generators in terms of functions on 4-dimensional real phase space is given with a realization of the Lie product in terms of Poisson brackets. This is the classical Jordan–Schwinger map which is also given for the deformed algebras SL q (2, ...

A possible notion of superspace associated to a given 3-dimensional Lie algebra g0 might be a Lie superalgebra g g0 ⊕ g1. If one is to introduce a minimal set of assumptions, it seems quite natural to consider those superalgebras for which g1 g0 and for which the g0 action on g1 is the adjoint representation. A complete classification of the real and complex 3, 3 -dimensional Lie superalgebras ...

In this paper a particular case of z-ideals, called strongly z-ideal, is defined by introducing zero sets in pointfree topology. We study strongly z-ideals, their relation with z-ideals and the role of spatiality in this relation. For strongly z-ideals, we analyze prime ideals using the concept of zero sets. Moreover, it is proven that the intersection of all zero sets of a prime ideal of C(L),...