Related papers: The Cantor-Bernstein-Schroder theorem in algebra

Domain theory has its origins in Mathematics and Theoretical Computer Science. Mathematically it combines order and topology. Its central concepts have their origin in the idea of approximating ideal objects by their relatively finite or,…

The Lie algebra generated by supertranslation and superrotation vector fields at null infinity, known as the extended BMS (eBMS) algebra is expected to be a symmetry algebra of the quantum gravity S matrix. However, the algebra of…

Schmidt's subspace theorem in terms of Seshadri constants for closed subschemes in subgeneral position has been already developed sharply. We derive our theorem for numerically equivalent ample divisors by dint of the above theory step by…

We establish a formula for the L-theory spectrum of real $C^*$-algebras from which we deduce a presentation of the L-groups in terms of the topological K-groups, extending all previously known results of this kind. Along the way, we extend…

The Burger-Sarnak method shows that the restriction of an automorphic representation of a reductive group to a reductive subgroup has automorphic support. Clozel has conjectured a qualitative refinement of this result, which were first…

We generalize the reciprocity theorem of G.R.~Robinson, D. Benson and P. Webb between a finite group and its subgroup to the case of finite-dimensional {\it symmetric} algebras over a field which are connected by a bimodule for the two…

In this work we will investigate a certain generalization of the so called S-lemma in higher degrees. The importance of this generalization is, that it is closely related to Hilbert's 1888 theorem about tenary quartics. In fact, if such a…

In this work we present a BMS-like ansatz for a Chern-Simons theory based on the semi-simple enlargement of the Poincar\'e symmetry, also known as AdS-Lorentz algebra. We start by showing that this ansatz is general enough to contain all…

The report below describes the applications of Banach KK-theory to a conjecture of P. Baum and A. Connes about the K-theory of group $C^*$-algebras, and a new proof of the classification by Harish-Chandra, the construction by Parthasarathy…

H.Furstenberg and E.Glasner proved that for an arbitrary $k\in\mathbb{N}$, any piecewise syndetic set of integers contains a $k$-term arithmetic progression and the collection of such progressions is itself piecewise syndetic in…

We prove the $K$-theoretic Farrell-Jones conjecture for groups as in the title with coefficient rings and $C^*$-algebras which are stable with respect to compact operators. We use this and Higson-Kasparov's result that the Baum-Connes…

It is known from Grzegorczyk's paper \cite{grze-1951} that the lattice of real semi-algebraic closed subsets of ${\mathbb R}^n$ is undecidable for every integer $n\geq 2$. More generally, if $X$ is any definable set over a real or…

After substantial progress over the last 15 years, the "algebraic CSP-dichotomy conjecture" reduces to the following: every local constraint satisfaction problem (CSP) associated with a finite idempotent algebra is tractable if and only if…

The cyclotomic Birman-Murakami-Wenzl (BMW) algebras B_n^k, introduced by R. H\"aring-Oldenburg, are a generalisation of the BMW algebras associated with the cyclotomic Hecke algebras of type G(k,1,n) (aka Ariki-Koike algebras) and type B…

A generalised notion of Kac-Moody algebra is defined using smooth maps from a compact real manifold $\mathcal{M}$ to a finite-dimensional Lie group, by means of complete orthonormal bases for a Hermitian inner product on the manifold and a…

An intriguing feature of positive $C_0$-semigroups on function spaces (or more generally on Banach lattices) is that their long-time behaviour is much easier to describe than it is for general semigroups. In particular, the convergence of…

We show that the strongly symmetric spectral convex compact sets are precisely the normalized state spaces of finite-dimensional simple Euclidean Jordan algebras and the simplices. Spectrality is the property that every state has a convex…

We define the filtrated K-theory of a C*-algebra over a finite topological space X and explain how to construct a spectral sequence that computes the bivariant Kasparov theory over X in terms of filtrated K-theory. For finite spaces with…

In this paper, we collect some technical results about weights on C*-algebras which are useful in de theory of locally compact quantum groups in the C*-algebra framework. We discuss the extension of a lower semi-continuous weight to a…

We prove a spectral theorem for bimodules in the context of graph C*-algebras. A bimodule over a suitable abelian algebra is determined by its spectrum (i.e., its groupoid partial order) iff it is generated by the Cuntz-Krieger partial…