( b ) H is maximal n i l p o t e n t and every subgroup of f i n i t e l a d e x . . i s of f i n i t e index i n i t s normalizer. Proof of Theorem 6: ( a ) Map Ga -> #, by x,: t -> x,(t) . This is a r a t i o n a l homomorphism. So s i n c e Ga i s a connected , ~ g e b r a i c group s o i s Xa . Hence G is a lgebra ic and connected.. Let R = r a d G . Since R is so lvable and normal it i s f...

‎let $mathcal{a}$ be a unital banach algebra‎, ‎$mathcal{m}$ be a left $mathcal{a}$-module‎, ‎and $w$ in $mathcal{z}(mathcal{a})$ be a left separating point of $mathcal{m}$‎. ‎we show that if $mathcal{m}$ is a unital left $mathcal{a}$-module and $delta$ is a linear mapping from $mathcal{a}$ into $mathcal{m}$‎, ‎then the following four conditions are equivalent‎: ‎(i) $delta$ is a jordan left de...

In this article, we introduce monomial irreducible representations of the special linear Lie algebra $sln$. We will show that this kind of representations have bases for which the action of the Chevalley generators of the Lie algebra on the basis elements can be given by a simple formula.

studied by Kazhdan and Lusztig in [KL88]. For x = gG(O) ∈ X the G(O)-orbit (for the adjoint action) of Ad(g)(u) in g(O) depends only on x, and its image under g(O) ։ g(C) is a well-defined G(C)orbit in g(C). We say that x ∈ X is regular if the associated orbit is regular in g(C). (Recall that an element of g(C) is regular if the nilpotent part of its Jordan decomposition is a principal nilpoten...

We determine and classify all finite-dimensional Hopf algebras over an algebraically closed field of characteristic zero whose coradicals are isomorphic to dual Radford dimension $4p$ for a prime $p>5$. In particular, we obtain families new examples without the Chevalley property.

The notion of a signed measure arises if a measure is allowed to take on both positive and negative values. A set that is both positive and negative with respect to a signed measure is termed as a null set. Some concepts in measure theory can be generalized by means of classes of null sets. An abstract formulation and proof of the Lebesgue decomposition theorem using the concept of null sets is...

Let M be a von Neumann algebra (not necessarily semi-finite). We provide a generalization of the classical Kadec-Pe lczynski subsequence decomposition of bounded sequences in L[0, 1] to the case of the Haagerup L-spaces (1 ≤ p < ∞). In particular, we prove that if (φn)n is a bounded sequence in the predual M∗ of M, then there exist a subsequence (φnk)k of (φn)n, a decomposition φnk = yk + zk su...

The convex and metric structures underlying probabilistic physical theories are generally described in terms of base normed vector spaces. According to a recent proposal, the purely geometrical features of these spaces are appropriately represented in terms of the notion of measure cone and the mixing distance [1], a specification of the novel concept of direction distance [2]. It turns out tha...