In our preceding paper we have introduced the notion of an s-homogeneous triple. this use technique to study connected algebras with two relations. For such algebras, describe all possible pairs (A,M), where A is s-Veronese ring and M (s,1)-Veronese bimodule dual algebra. each a pair classify corresponding or give necessary sufficient conditions for algebra under consideration correspond given ...

The aim of this sequel to arXiv:1812.02935 is set up the cornerstones Koszul duality and Koszulity in context operads over a large class operadic categories. In particular, for these categories we will study concrete examples binary quadratic operads, describe their duals prove that they are Koszul. This includes whose algebras most important operad- PROP-like structures such as classical varia...

The François Massieu 1869 idea to derive some mechanical and thermal properties of physical systems from “Characteristic Functions”, was developed by Gibbs and Duhem in thermodynamics with the concept of potentials, and introduced by Poincaré in probability. This paper deals with generalization of this Characteristic Function concept by Jean-Louis Koszul in Mathematics and by Jean-Marie Souriau...

A. Kurosh's theorem for groups [4] provides the structure of any subgroup a free product and its proof relies on Bass-Serre theory acting trees. In case Lie algebras, such general does not exist analogue Kurosh is false in general, as it was first noticed by A.I. Shirshov [10]. However, we prove that, class positively graded algebras satisfying certain local properties cohomology, holds true su...