Projectively equivariant quantizations over the superspace Rp∣q\R^{p|q}

We investigate the concept of projectively equivariant quantization in the framework of super projective geometry. When the projective superalgebra pgl(p+1|q) is simple, our result is similar to the classical one in the purely even case: we prove the existence and uniqueness of the quantization except in some critical situations. When the projective superalgebra is not simple (i.e. in the case of pgl(n|n)\not\cong sl(n|n)), we show the existence of a one-parameter family of equivariant quantizations. We also provide explicit formulas in terms of a generalized divergence operator acting on supersymmetric tensor fields.Comment: 19 page

The ternary invariant differential operators acting on the spaces of weighted densities

Over n-dimensional manifolds, I classify ternary differential operators acting on the spaces of weighted densities and invariant with respect to the Lie algebra of vector fields. For n=1, some of these operators can be expressed in terms of the de Rham exterior differential, the Poisson bracket, the Grozman operator and the Feigin-Fuchs anti-symmetric operators; four of the operators are new, up to dualizations and permutations. For n>1, I list multidimensional conformal tranvectors, i.e.,operators acting on the spaces of weighted densities and invariant with respect to o(p+1,q+1), where p+q=n. Except for the scalar operator, these conformally invariant operators are not invariant with respect to the whole Lie algebra of vector fields.Comment: 13 pages, no figures, to appear in Theor. Math. Phy

Two problems about perfect distributive lattices

SIGLETIB: RN 3109 (201) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Easkia Duality and Its Extensions

In recent years Esakia duality for Heyting algebras has been extended in two directions. First to weak Heyting algebras, namely distributive lattices with an implication with weaker properties than that of the implication of a Heyting algebra, and secondly to implicative semilattices. The first algebras correspond to subintuitionistic logics, the second ones to the conjunction and implication fragment of intuitionistic logic. Esakia duality has also been complemented with dualities for categories whose objects are Heyting algebras and whose morphisms are maps that preserve less structure than homomorphisms of Heyting algebras. In this paper we survey these developments.Fil: Celani, Sergio Arturo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Tandil; Argentina. Universidad Nacional del Centro de la Provincia de Buenos Aires. Facultad de Ciencias Exactas. Núcleo Consolidado de Matemática Pura y Aplicada; ArgentinaFil: Jansana Ferrer, Ramon. Universidad de Barcelona; Españ

On Finite-Valued Bimodal Logics with an Application to Reasoning About Preferences

In a previous paper by Bou et al., the minimal modal logic over a finite residuated lattice with a necessity operator was characterized under different semantics. In the general context of a residuated lattice, the residual negation ¬ is not necessarily involutive, and hence a corresponding possibility operator cannot be introduced by duality. In the first part of this paper we address the problem of extending such a minimal modal logic with a suitable possibility operator Q. In the second part of the paper, we introduce suitable axiomatic extensions of the resulting bimodal logic and define a logic to reason about fuzzy preferences, generalising to the many-valued case a basic preference modal logic considered by van Benthem et al. © Springer International Publishing AG 2018Vidal acknowledges support by the joint project Austrian Science Fund (FWF) I1897-N25 and Czech Science Foundation (GACR) 15-34650L, and by the institutional grant RVO:67985807. Esteva and Godo acknowledge support by the FEDER/MINECO project TIN2015-71799-C2-1-PPeer Reviewe