Related papers: A Product Theorem in simple Lie groups

We prove that the 2-Deligne tensor product of two compact semisimple 2-categories exists. Further, under suitable hypotheses, we explain how to describe the $Hom$-categories, connected components, and simple objects of a 2-Deligne tensor…

We generalize the Cauchy-Davenport theorem to locally compact groups.

We establish some results about large restricted Lie algebras similar to those known in the Group Theory. As an application we use this group-theoretic approach to produce some examples of restricted as well as ordinary Lie algebras which…

Liebeck, Nikolov, and Shalev conjectured that for every subset A of a finite simple group S with |A|>1, there exist O( log|S| / log|A| ) conjugates of A whose product is S. This paper is a companion to [Lifshitz: Completing the proof of the…

We prove that the greedy sum of a direct product of two numeric arrays of complex numbers is equal to the product of the greedy sums of the factors provided that all the mentioned sums exist.

We present a new method to bound the cardinality of triple product sets in groups and give three applications. A new and unexpectedly short proof of the Plunnecke-Ruzsa sumset inequalities for Abelian groups. A new proof of a theorem of Tao…

We prove that every finite direct product of crystallographic groups arising from an irreducible root system (in the sense of Lie theory) is profinitely rigid (equiv. first-order rigid). This is a generalization of recent proofs of…

The note provides a simple proof of Kisin's theorem about the restriction of crystalline representations to certain subgroup of the Galois group.

We present an exposition of the Auinger-Steinberg proof of the Ribes-Zalesski\u{i} product theorem for pro-V topologies, where V is a pseudovariety of groups closed under extensions with abelian kernel. This proof is self-contained and is…

A detailed proof of a recent result on explicit formulae for the product moments $E \left \{ X_1^{a_1} X_2^{a_2} \cdots X_n^{a_n}\right \}$ of multivariate Gaussian random variables is provided in this note.

In this paper we define a new algebraic object: the disguised-groups. We show the main properties of the disguised-groups and, as a consequence, we will see that disguised-groups coincide with regular semigroups. We prove many of the…

In the present paper we prove Liouville-type theorems: non-existence theorems for complete twisted and warped products of Riemannian manifolds which generalize and complement similar results for compact manifolds.

We establish a general spectral gap theorem for actions of products of groups which may replace Kazhdan's property (T) in various situations. As a main application, we prove that a confined subgroup of an irreducible lattice in a higher…

We prove some results of Kemperman--Scherk type for restricted product sets in multiplicative groups of fields (in particular, for cyclic groups). The proofs use polynomial method.

A discrete group is said to be C*-simple if its reduced C*-algebra is simple, and is said to have the unique trace property if its reduced C*-algebra has a unique tracial state. A dynamical characterization of C*-simplicity was recently…

We prove a formula expressing the $K$-theoretic log Gromov-Witten invariants of a product of log smooth varieties $V \times W$ in terms of the invariants of $V$ and $W$. The proof requires introducing log virtual fundamental classes in…

For every Lie group $G$, we compute the maximal $n$ such that an $n$-fold product of nonabelian free groups embeds into $G$.

We introduce the notion of a bicocycle double cross product (resp. sum) Lie group (resp. Lie algebra), and a bicocycle double cross product bialgebra, generalizing the unified products. On the level of Lie groups the construction yields a…

For the free group on n generators we prove that the discrete logarithm is distributed according to the standard Gaussian when the logarithm is renormalized appropriately.

Given two convex polytopes, the join, the cartesian product and the direct sum of them are well understood. In this paper we extend these three kinds of products to abstract polytopes and introduce a new product, called the topological…