Ge asked the question whether $LF_{\infty}$ can be embedded into $LF_2$ as a maximal subfactor. We answer it affirmatively by three different approaches, all containing same key ingredient: existence of subgroups with infinite index. also show that point stabilizer for every faithful, 4-transitive action on an set give rise to von Neumann subalgebras. Combining this known results constructing h...

Let k k be any field and let alttext="upper G"> G encoding="application/x-tex">G a connected reductive alge...

The five simple exceptional complex Lie superalgebras of vector fields are described. One of them, kas, is new; the other four are explicitly described for the first time. All nonisomorphic maximal subalgebras of finite codimension of these Lie superalgebras, i.e., all other realizations of these Lie superalgebras as Lie superalgebras of vector fields, are also described; there are 14 of them a...

In this paper we prove that for a type II1 factor N with a Cartan maximal abelian subalgebra (masa), the Hochschild cohomology groups Hn(N, N)=0, for all n ≥ 1. This generalizes the result of Sinclair and Smith, who proved this for all N having separable predual.

We show that in the one-dimensional case the weighted Hardy–Littlewood maximal operator Mμ is bounded on BMO(μ) for arbitrary Radon measure μ, and that this is not the case in higher dimensions.

In this paper we consider Q the class of solvable Lie algebras L with the following property: if A is a subalgebra of L, then Φ(A) ⊆ Φ(L) (where Φ(L) denotes the Frattini subalgebra of L;that is Φ(L) is the intersection of all maximal subalgebras of L). The class Q is shown to contain all solvable Lie algebras whose derived algebra is nilpotent. Necessary conditions are found such that an ideal...