Related papers: A complete Heyting algebra whose Scott space is no…

In this paper, we will focus on k-bounded sober spaces and show the existence of a T_0 space X not admitting any k-bounded sobrification. This strengthens a result of Zhao, Lu and Wang, who proved that the canonical k-bounded sobrification…

We affirm a conjecture of Sacks [1972] by showing that every countable distributive lattice is isomorphic to an initial segment of the hyperdegrees, $\mathcal{D}_{h}$. In fact, we prove that every sublattice of any hyperarithmetic lattice…

Let $Q$ be a subset of a finite distributive lattice $D$. An algebra $A$ represents the inclusion $Q\subseteq D$ by principal congruences if the congruence lattice of $A$ is isomorphic to $D$ and the ordered set of principal congruences of…

In this paper, we first classify all irreducible modules of the vertex algebra $V_L^+$ when $L$ is a negative definite even lattice of arbitrary rank. In particular, we show that any irreducible $V_L^+$-module is isomorphic to a submodule…

Motivated by the Hilbert-space model for quantum mechanics, we define a pre-Hilbert space logic to be a pair $(S,\el)$, where $S$ is a pre-Hilbert space and $\el$ is an orthocomplemented poset of orthogonally closed linear subspaces of $S$,…

We prove that, for every Coxeter diagram $D$ with no rank $3$ residues of spherical type and such that $D$ has not only edges labelled by $2$, the space of countable (Tits) buildings of type $D$ is Borel complete, that is, classifying…

Brauer and Thrall conjectured that a finite-dimensional algebra over a field of bounded representation type is actually of finite representation type and a finite-dimensional algebra (over an infinite field) of infinite representation type…

We prove that any finite subdirectly irreducible Heyting algebra with involution is quasi-primal, and that injective algebras in the variety generated by a finite subdirectly irreducible Heyting algebra are precisely diagonal subalgebras of…

We construct a distributive algebraic lattice D that is not isomorphic to the congruence lattice of any lattice. This solves a long-standing open problem, traditionally attributed to R. P. Dilworth, from the forties. The lattice D has…

Let H_1 and H_2 be complex Hilbert spaces, L_1=P(H_1) and L_2=P(H_2) the lattices of closed subspaces, and let L be a complete atomistic lattice. We prove under some weak assumptions relating L_i and L, that if L admits an…

In this paper it is shown that the lattice of C*-covers of an operator algebra does not contain enough information to distinguish operator algebras up to completely isometric isomorphism. In addition, four natural equivalences of the…

Let A be an abelian category of finite type and homological dimension 1. Then by results of Green R(A), the extended Hall-Ringel algebra of A, has a natural Hopf algebra structure. We consider its Heisenberg double Heis(A) and study its…

Let G be a connected reductive group over a non-archimedean local field. We say that an irreducible depth-zero (complex) G-representation is non-singular if its cuspidal support is non-singular. We establish a Local Langlands Correspondence…

We establish a bijective correspondence between isomorphism classes of basic silting objects of $\mathsf{per}(A)$ and algebraic $t$-structures of $\mathsf{D}_{\rm fd}(A)$ for locally finite non-positive dg algebra $A$ over a field $k$ (more…

We examine the properties of algebras of linear transformations that leave invariant all subspaces in a totally ordered lattice of subspaces of an arbitrary vector space. We compare our results with those that apply for the corresponding…

Let $L$ be an even, hyperbolic lattice with infinitely many simple $(-2)$-roots. We call $L$ a Borcherds lattice if it admits an isotropic vector with bounded inner product with all the simple $(-2)$-roots. We show that this is the case if…

Let R be a von Neumann algebra acting on a Hilbert space H and let R_sa be the set of selfadjoint elements of R. It is well known that R_sa is a lattice with respect to the usual partial order ≤ if and only if R is abelian. We define…

If $Q$ is a surjection from $L^1(\mu)$, $\mu$ $\sigma$-finite, onto a Banach space containing $c_0$ then (*) $\ker Q$ is uncomplemented in its second dual. If $Q$ is a surjection from an ${\cal L}_1$-space onto a Banach space containing…

Let G be a reductive group over a commutative ring R. We say that G has isotropic rank >=n, if every normal semisimple reductive R-subgroup of G contains (G_m)^n. We prove that if G has isotropic rank >=1 and R is a regular domain…

We study moduli spaces of lattice-polarized K3 surfaces in terms of orbits of representations of algebraic groups. In particular, over an algebraically closed field of characteristic 0, we show that in many cases, the nondegenerate orbits…