Related papers: Implicative algebras II: completeness w.r.t. Set-b…

We show that the isomorphism class of a two-step solvable Lie poset subalgebra of a semisimple Lie algebra is determined by its dimension. We further establish that all such algebras are absolutely rigid.

Given a finite-dimensional, complex simple Lie algebra we exhibit an integral form for the universal enveloping algebra of its map algebra, and an explicit integral basis for this integral form. We also produce explicit commutation formulas…

We extend the meet-implication fragment of propositional intuitionistic logic with a meet-preserving modality. We give semantics based on semilattices and a duality result with a suitable notion of descriptive frame. As a consequence we…

We give a complete classification (up to isomorphism) of Lie conformal algebras which are free of rank two as $\C[\partial]$-modules, and determine their automorphism groups.

Let $X$ be a locally finite preordered set, $\mathcal R$ a commutative ring with identity and $I(X,\mathcal R)$ the incidence algebra of $X$ over $\mathcal R$. In this note we prove that each Lie derivation of $I(X,\mathcal R)$ is proper,…

We discuss how triposes may be understood as generalizations of localic geometric morphisms.

We call a poset factorable if its characteristic polynomial has all positive integer roots. Inspired by inductive and divisional freeness of a central hyperplane arrangement, we introduce and study the notion of inductive posets and their…

In this paper we investigate the general combinatorical structure of the truth tables of all bracketed formulae with n distinct variables connected by the binary connective of implication, an m-implication.

Base on a conjecture, we prove that for any smooth separated stack of finite type over a number field, its descent obstruction equals its iterated descent obstruction. As a consequence, we show that for any algebraic stack over a number…

Using the notion of existentially closed structures, we obtain embedding theorems for groups and Lie algebras. We also prove the existence of some groups and Lie algebras with prescribed properties.

We show that every finite Abelian algebra A from congruence-permutable varieties admits a full duality. In the process, we prove that A also allows a strong duality, and that the duality may be induced by a dualizing structure of finite…

We employ the notions of `sequential function' and `interrogation' (dialogue) in order to define new partial combinatory algebra structures on sets of functions. These structures are analyzed using J. Longley's preorder-enriched category of…

We give a survey on the theory of representation-finite and certain minimal representation-infinite algebras.The main goals are the existence of multiplicative bases and of coverings with good properties. Both are attained via…

We prove that all cubulated groups are semistable at infinity. In doing so we prove two further results about cubulations of groups. The first of these states that any one-ended cubulated group has a cubulation for which all halfspaces are…

We introduce decomposition complexes of posets, which generalize order complexes. The main advantage of our construction is that decomposition complexes are closed under taking products. Other special instances of this theory include nested…

We consider extension of a closure system on a finite set S as a closure system on the same set S containing the given one as a sublattice. A closure system can be represented in different ways, e.g. by an implicational base or by the set…

It is proved that any infinite Abelian group of infinite exponent admits a non-discrete reflexive group topology.

We use model theoretic techniques to construct explicit first-order axiomatizations for the classes of posets that can be represented as systems of sets, where the order relation is given by inclusion, and existing meets and joins of…

We study $Q$-tableaux and axiom systems that they engender, producing a new proof that the Implicational Propositional Calculus is complete.

We define analytic indices which involve the eta form and the analytic torsion form. We show that these indices are independent of the geometric choices made in their definitions, and hence are topological in nature.