Lattice of closure endomorphisms of a Hilbert algebra

A closure endomorphism of a Hilbert algebra A is a mapping that is simultaneously an endomorphism of and a closure operator on A. It is known that the set CE of all closure endomorphisms of A is a distributive lattice where the meet of two elements is defined pointwise and their join is given by their composition. This lattice is shown in the paper to be isomorphic to the lattice of certain filters of A, anti-isomorphic to the lattice of certain closure retracts of A, and compactly generated. The set of compact elements of CE coincides with the adjoint semilattice of A, conditions under which two Hilbert algebras have isomorphic adjoint semilattices (equivalently, minimal Brouwerian extensions) are discussed. Several consequences are drawn also for implication algebras.Comment: 16 pages, no figures, submitted to Algebra Universalis (under review since 24.11.2015

Localization of semi-Heyting algebras

In this note, we introduce the notion of ideal on semi-Heyting algebras which allows us to consider a topology on them. Besides, we define the concept of F−multiplier, where F is a topology on a semi-Heyting algebra L, which is used to construct the localization semi-Heyting algebra LF. Furthermore, we prove that the semi-Heyting algebra of fractions LS associated with an ∧−closed system S of L is a semi-Heyting of localization. Finally, in the finite case we prove that LS is isomorphic to a special subalgebra of L. Since Heyting algebras are a particular case of semi-Heyting algebras, all these results generalize those obtained in [11].Fil: Figallo, Aldo Victorio. Universidad Nacional de San Juan. Facultad de Filosofía, Humanidades y Artes. Instituto de Ciencias Básicas; ArgentinaFil: Pelaitay, Gustavo Andrés. Universidad Nacional de San Juan. Facultad de Filosofía, Humanidades y Artes. Instituto de Ciencias Básicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Juan; Argentina. Universidad Nacional de San Juan. Facultad de Filosofía, Humanidades y Artes. Departamento de Matemática; Argentin

On the structure of the essential spectrum of elliptic operators on metric spaces

We give a description of the essential spectrum of a large class of operators on metric measure spaces in terms of their localizations at infinity. These operators are analogues of the elliptic operators on Euclidean spaces and our main result concerns the ideal structure of the $C^*$-algebra generated by them.Comment: Improved presentation, some new results

Maximal C*-algebras of quotients and injective envelopes of C*-algebras

A new C*-enlargement of a C*-algebra $A$ nested between the local multiplier algebra $M_{\text{loc}}(A)$ of $A$ and its injective envelope $I(A)$ is introduced. Various aspects of this maximal C*-algebra of quotients, $Q_{\text{max}}(A)$, are studied, notably in the setting of AW*-algebras. As a by-product we obtain a new example of a type I C*-algebra $A$ such that $M_{\text{loc}}(M_{\text{loc}}(A))\ne M_{\text{loc}}(A)$.Comment: 37 page

Stratifying quotient stacks and moduli stacks

Recent results in geometric invariant theory (GIT) for non-reductive linear algebraic group actions allow us to stratify quotient stacks of the form [X/H], where X is a projective scheme and H is a linear algebraic group with internally graded unipotent radical acting linearly on X, in such a way that each stratum [S/H] has a geometric quotient S/H. This leads to stratifications of moduli stacks (for example, sheaves over a projective scheme) such that each stratum has a coarse moduli space.Comment: 25 pages, submitted to the Proceedings of the Abel Symposium 201