Related papers: Ultracontact algebras and stack systems
Contact Boolean algebras are one of the main algebraic tools in region-based theory of space. T. Ivanova provided strong motivations for the study of merely semilattices with a contact relation. Another significant motivation for…
Extending recent investigations on the structure of Tukey types of ultrafilters on $\mathcal{P}(\omega)$ to Boolean algebras in general, we classify the spectra of Tukey types of ultrafilters for several classes of Boolean algebras,…
After recalling the notion of Lie algebroid, we construct these structures associated with contact forms or systems. We are then interested in particular classes of Lie Rinehart algebras.
We study contact resolutions of Jacobi structures which are contact on an open subset. We give several classes of examples, as well as classes for which it cannot exist.
Motivated by some recent developments in abstract theories of quadratic forms, we start to develop in this work an expansion of Linear Algebra to multivalued structures (a multialgebraic structure is essentially an algebraic structure but…
We establish a relation between higher contact-like structures on supermanifolds and the N = 1 super-Poincare group via its superspace realisation. To do this we introduce a vector-valued contact structure, which we refer to as a…
We reexamine the relation between contact structures on supermanifolds and supersymmetric mechanics in the superspace formulation. This allows one to use the language of contact geometry when dealing with the d = 1, N = 2 super-Poincare…
We devise exact conditions under which a join semilattice with a weak contact relation can be semilattice embedded into a Boolean algebra with an overlap contact relation, equivalently, into a distributive lattice with additive contact…
We discuss the notion of the universal relatively hyperbolic structure on a group which is used in order to characterize relatively hyperbolic structures on the group. We also study relations between relatively hyperbolic structures on a…
In view of applications to the construction of moduli spaces of objects in algebraic supergeometry, we start a systematic study of stacks in that context. After defining a superstack as a stack over the \'etale site of superschemes, we…
In this paper we show how the hyperstructure concept leads to new algebraic structures and general field theories.
A notion of an algebroid - a generalization of a Lie algebroid structure is introduced. We show that many objects of the differential calculus on a manifold M associated with the canonical Lie algebroid structure on T^M can be obtained in…
We give simple characterizations of contact 1-forms in terms of Dirac structures. We also relate normal almost contact structures to the theory of Dirac structures.
The notion of a complete Boolean algebra, although completely legitimate in constructive mathematics, fails to capture some natural structures such as the lattice of subsets of a given set. Sambin's notion of an overlap algebra, although…
A general theory of the Frolicher-Nijenhuis and Schouten-Nijenhuis brackets in the category of modules over a commutative algebra is described. Some related structures and (co)homology invariants are discussed, as well as applications to…
We study integrability of generalized almost contact structures, and find conditions under which the main associated maximal isotropic vector bundles form Lie bialgebroids. These conditions differentiate the concept of generalized contact…
In this paper we develop a method for studying tight contact structures on lens spaces. We then derive uniqueness and non-existence statements for tight contact structures with certain (half) Euler classes on lens spaces. We also prove that…
This is an expository article on the theory of algebraic stacks. After introducing the general theory, we concentrate in the example of the moduli stack of vector budles, giving a detailed comparison with the moduli scheme obtained via…
We consider the Lie algebra of all vector fields on a contact manifold as a module over the Lie subalgebra of contact vector fields. This module is split into a direct sum of two submodules: the contact algebra itself and the space of…
We define and study complex structures and generalizations on spaces consisting of geodesics or harmonic maps that are compatible with the symmetries of these spaces. The main results are about existence and uniqueness of such structures.