Related papers: A universal Kaluzhnin--Krasner embedding theorem

Let H be a non semi-simple Ariki-Koike algebra. According to [18] and [14], there is a generalisation of Lusztig's a-function which induces a natural order (parametrised by a tuple m) on Specht modules. In some cases, Geck and Jacon have…

Lie's Third Theorem, asserting that each finite-dimensional Lie algebra is the Lie algebra of a Lie group, fails in infinite dimensions. The modern account on this phenomenon is the integration problem for central extensions of…

In our preceding papers we started considering the categories of tangles with flat G-connections in their complements, where G is a simple complex algebraic group. The braiding (or the commutativity constraint) in such categories satisfies…

We give a proof of the Universality Conjecture for orthogonal and symplectic ensembles of random matrices in the scaling limit for a class of weights w(x)=exp(-V(x)) where V is a polynomial, V(x)=kappa_{2m}x^{2m}+..., kappa_{2m}>0. For such…

C. Schochet shows K\"unneth theorem for the $C^*$-algebras in the smallest class of nuclear $C^*$-algebras which contains the separable Type I algebras and is closed under some operations. We calculate the $K$-theory for the crossed product…

We consider the class of crossed products of noetherian domains with universal enveloping algebras of Lie algebras. For algebras from this class we give a sufficient condition for the existence of projective non-free modules. This class…

Let $A$ be a separable amenable $C^*$-algebra and $B$ a non-unital and $\sigma$-unital simple $C^*$-algebra with continuous scale ($B$ need not be stable). We classify, up to unitary equivalence, all essential extensions of the form $0…

The general class of the graded Lie algebras is defined. These algebras could be constructed using an arbitrary dynamical systems with discrete time and with invarinat measure. In this papers we consider the case of the central extension of…

We prove that every positive trace on a countably generated *-algebra can be approximated by positive traces on algebras of generic matrices. This implies that every countably generated tracial *-algebra can be embedded into a metric…

We introduce a notion of $n$-Lie Rinehart algebras as a generalization of Lie Rinehart algebras to $n$-ary case. This notion is also an algebraic analogue of $n$-Lie algebroids. We develop representation theory and describe a cohomology…

In this paper we provide several \emph{metric universality} results. We exhibit for certain classes $\cC$ of metric spaces, families of metric spaces $(M_i, d_i)_{i\in I}$ which have the property that a metric space $(X,d_X)$ in $\cC$ is…

The theory of algebraic extensions of Banach algebras is well established, and there are many constructions which yield interesting extensions. In particular, Cole's method for extending uniform algebras by adding square roots of functions…

Let $(X,T)$ be a dynamical system where $X$ is a compact metric space and $T:X\rightarrow X$ is continuous and invertible. Assume the Lebesgue covering dimension of $X$ is $d$. We show that for a generic continuous map…

We show that the Baum--Connes assembly map factors canonically through the unitary conjugation groupoid, which serves as a universal mediator among groupoid models that are Morita equivalent to a given transformation groupoid. This…

This paper develops a categorical framework to clarify the relationship between the completeness and compactness theorems in classical first-order logic. Rather than claiming that different model constructions yield naturally isomorphic…

We present a short and clear proof of the following particular case of a 2006 result of Melikhov-Schepin: Let $K$ be a $k$-dimensional simplicial complex and $K*[3]$ the union of three cones over $K$ along their common bases. If $2d\ge3k+3$…

The Yang-Baxter equation plays a fundamental role in various areas of mathematics. Its solutions, called braidings, are built, among others, from Yetter-Drinfel'd modules over a Hopf algebra, from self-distributive structures, and from…

Using elementary equalities between various cables of the unknot and the Hopf link, we prove the Wheels and Wheeling conjectures of [Bar-Natan, Garoufalidis, Rozansky and Thurston, arXiv:q-alg/9703025] and [Deligne, letter to Bar-Natan,…

Cuntz algebras $\mathcal{O}_n$, $n>1$, are celebrated examples of a separable infinite simple C*-algebra with a number of fascinating properties. Their K-theory allows an embedding of $\mathcal O_m$ in $\mathcal O_n$ whenever $n-1$ divides…

A theorem by Mumford implies that every automorphic line bundle on a pure open Shimura variety, equipped with an invariant smooth metric, can be uniquely extended as a line bundle on a toroidal compactification of the variety, in such a way…