On universal central extensions of Hom-Leibniz algebras

In the category of Hom-Leibniz algebras we introduce the notion of Hom-corepresentation as adequate coefficients to construct the chain complex from which we compute the Leibniz homology of Hom-Leibniz algebras. We study universal central extensions of Hom-Leibniz algebras and generalize some classical results, nevertheless it is necessary to introduce new notions of α-central extension, universal α-central extension and α-perfect Hom-Leibniz algebra due to the fact that the composition of two central extensions of Hom-Leibniz algebras is not central. We also provide the recognition criteria for these kind of universal central extensions. We prove that an α-perfect Hom-Lie algebra admits a universal α-central extension in the categories of Hom-Lie and Hom-Leibniz algebras and we obtain the relationships between both of them. In case α = Id we recover the corresponding results on universal central extensions of Leibniz algebras.

Type checking cryptography implementations

Cryptographic software development is a challenging eld: high performance must be achieved, while ensuring correctness and com- pliance with low-level security policies. CAO is a domain speci c language designed to assist development of cryptographic software. An important feature of this language is the design of a novel type system introducing native types such as prede ned sized vectors, matrices and bit strings, residue classes modulo an integer, nite elds and nite eld extensions, allowing for extensive static validation of source code. We present the formalisation, validation and implementation of this type system

A taxonomy for virtual enterprises

The purpose of this paper is to present a taxonomy able to contribute to building a framework within the domain of Virtual Enterprises (VE), to facilitate the sharing of knowledge and contributions to knowledge, as well as for trust building among VE stakeholders. A VE taxonomy currently does not exist, and this lack is felt in the ambiguous way that some concepts are addressed, leading to a fragment understanding that hinders the development of the science of VE integration and management. The structure of the taxonomy developed is based on the view of the system as a 5-tuple consisting of Input, Control, Output, Mechanism, and Process, which is the underlying system-view in the well-know IDEF0 diagramming technique. In particular, this taxonomy addresses the VE extended lifecycle that implies the use of a meta-organization called Market of Resources, as an original contribution to the VE theory and practice. The taxonomy presented does not repeat what the literature already includes, or the commonplaces, and it is constructed in a way to be easily complemented with other VE partial taxonomies that may be found in literature. Some suggestions for extensions to other interrelated domains (as evolution leaves taxonomies in an open or incompleteness state) are given in the text.