Related papers: Relative algebroids and Cartan realization problem…

We define here the category of partial differential equations. Special cases of morphisms from an object (equation) are symmetries of the equation and reductions of the equation by a symmetry groups, but there are many other morphisms. We…

This is a survey article on real algebra and geometry, and in particular on its recent applications in optimization and convexity. We first introduce basic notions and results from the classical theory. We then explain how these relate to…

In this review we discuss what is known about semiorthogonal decompositions of derived categories of algebraic varieties. We review existing constructions, especially the homological projective duality approach, and discuss some related…

In this paper, we first give the definiton of a vertex superalgebroid. Then we construct a family of vertex superalgebras associated to vertex superalgebroids. As a main result, we find a sufficient and necessary condition that this vertex…

We study the relative modular classes of Lie algebroids, and we determine their relationship with the modular classes of Lie algebroids with a twisted Poisson structure.

The paper deals with a construction of a separating system of rational invariants for finite dimensional generic algebras. In the process of dealing an approach to a rough classification of finite dimensional algebras is offered by…

We discuss the local and global problems for the equivalence of geometric structures of an arbitrary order and, in later sections, attention is given to what really matters, namely the equivalence with respect to transformations belonging…

A geometric approach is used to study the Abel first order differential equation of the first kind. The approach is based on the recently developed theory of quasi-Lie systems which allows us to characterise some particular examples of…

In this paper we introduce the notion of generalized Lie algebroid and we develop a new formalism necessary to obtain a new solution for the Weistein's Problem. Many applications emphasize the importance and the utility of this new…

A new type of sectional curvature is introduced. The notion is purely algebraic and can be located in linear algebra as well as in differential geometry.

Real algebraic geometry adapts the methods and ideas from (complex) algebraic geometry to study the real solutions to systems of polynomial equations and polynomial inequalities. As it is the real solutions to such systems modeling…

We develop a random model for relation algebras. We prove some preliminary results and pose questions that lay out a new direction of research.

We combine two recent ideas: cartesian differential categories, and restriction categories. The result is a new structure which axiomatizes the category of smooth maps defined on open subsets of $\R^n$ in a way that is completely algebraic.…

Second-order superintegrable systems in dimensions two and three are essentially classified. With increasing dimension, however, the non-linear partial differential equations employed in current methods become unmanageable. Here we propose…

We introduce the notion of almost finite dimensionality of algebras and study its connection with the classical finiteness conditions.

Recently, relative Rota-Baxter (Lie/associative) algebras are extensively studied in the literature from cohomological points of view. In this paper, we consider relative Rota-Baxter Leibniz algebras (rRB Leibniz algebras) as the object of…

Motivated by applications in moduli theory, we introduce a flexible and powerful language for expressing lower bounds on relative dimension of morphisms of schemes, and more generally of algebraic stacks. We show that the theory is robust…

Reductions of higher tangent bundles of Lie groupoids provide natural examples of geometric structures which we would like to call higher algebroids. Such objects can be also constructed abstractly starting from an arbitrary almost Lie…

In this work, we introduce the concept of relative Lipschitz saturation, along with its key categorical and algebraic properties, and demonstrate how such a structure always gives rise to a radicial algebra.

We show how one can associate to a given class of finite type G-structures a classifying Lie algebroid. The corresponding Lie groupoid gives models for the different geometries that one can find in the class, and encodes also the different…