Related papers: Remarks on the diagonal embedding and strong 1-bou…

Supersymmetric domain walls are reviewed. The main emphasis is made on saturated walls in strongly coupled gauge theories. The central charge of the N=1 superalgebra appears in supersymmetric gluodynamics as a quantum anomaly. I also…

Engel subalgebras of finite-dimensional Leibniz algebras are shown to have similar properties to those of Lie algebras. Using these, it is shown that a left Leibniz algebra, all of whose maximal subalgebras are right ideals, is nilpotent. A…

The Cohn-Umans group-theoretic approach to matrix multiplication suggests embedding matrix multiplication into group algebra multiplication, and bounding $\omega$ in terms of the representation theory of the host group. This framework is…

Let $G$ be a group that is relatively hyperbolic with respect to a collection of subgroups $\{H_{\lambda}\}_{\lambda\in \Lambda}$. Suppose that $G$ is given by a finite relative presentation $\mathcal{P}$ with respect to this collection. We…

Let $V_{L}$ be the vertex algebra associated to a non-degenerate even lattice $L$, $\theta$ the automorphism of $V_{L}$ induced from the $-1$-isometry of $L$, and $V_{L}^{+}$ the fixed point subalgebra of $V_{L}$ under the action of…

We prove that connected higher rank simple Lie groups have Lafforgue's strong property (T) with respect to a certain class of Banach spaces $\mathcal{E}_{10}$ containing many classical superreflexive spaces and some non-reflexive spaces as…

In the framework of homological characterizations of relative hyperbolicity, Groves and Manning posed the question of whether a simply connected $2$-complex $X$ with a linear homological isoperimetric inequality, a bound on the length of…

The space spanned by the characters of twisted affine Lie algebras admit the action of certain congruence subgroups of $SL(2,\mathbb{Z})$. By embedding the characters in the space spanned by theta functions, we study an…

We prove there is a class of maps $\gamma:\mathbb{T}^{2n}\rightarrow\mathbb{S}^1$ such that a conservative dynamically coherent partially hyperbolic skew-product on $\mathbb{T}^{2n}\times\mathbb{S}^1$ with fixed hyperbolic dynamics on the…

In this paper, we introduce a notion of stable coarse algebras for metric spaces with bounded geometry, and formulate the twisted coarse Baum--Connes conjecture with respect to stable coarse algebras. We prove permanence properties of this…

We show that there are infinitely many commensurability classes of pseudomodular groups, thus answering a question raised by Long and Reid. These are Fuchsian groups whose cusp set is all of the rationals but which are not commensurable to…

We continue the study of supersymmetric domain wall solutions in six-dimensional maximal gauged supergravity. We first give a classification of viable gauge groups with the embedding tensor in $\mathbf{5}^{+7}$, $\bar{\mathbf{5}}^{+3}$,…

We study the existence of multiplier (completely) bounded approximate identities for the Fourier algebras of some classes of hypergroups. In particular we show that, a large class of commutative hypergroups are weakly amenable with the…

There exist principal $\mathfrak{sl}_2$ subalgebras for hyperbolic Kac-Moody Lie algebras. In the case of rank 2 symmetric hyperbolic Kac-Moody Lie algebras, certain $\mathfrak{sl}_2$ subalgebras are constructed. These subalgebras are…

The powerful group theoretical formalism of potential algebras is extended to non-Hermitian Hamiltonians with real eigenvalues by complexifying so(2,1), thereby getting the complex algebra sl(2,\C) or $A_1$. This leads to new types of both…

We show that a QWEP von Neumann algebra has the weak* positive approximation property if and only if it is seemingly injective in the following sense: there is a factorization of the identity of $M$ $$Id_M=vu: M{\buildrel…

We study the poset of hyperbolic structures on Thompson's group $F$ and its generalizations $F_n$ for $n \geq 2$. The global structure of this poset is as simple as one would expect, with the maximal non-elementary elements being two…

We establish a hypertrace characterization of property (T) for $\mathrm{II}_1$ factors: Given a $\mathrm{II}_1$ factors $M$, $M$ does not have property (T) if and only if there exists a von Neumann algebra $\mathcal{A}$ with $M\subset…

Let $G$ be a simple algebraic group over an algebraically closed field $K$ of characteristic $p > 0$. We consider connected reductive subgroups $X$ of $G$ that contain a given distinguished unipotent element $u$ of $G$. A result of…

This paper includes a series of structural results for von Neumann algebras arising from measure preserving actions by product groups on probability spaces. Expanding upon the methods used earlier by the first two authors \cite{CS}, we…