Related papers: Real algebraic structures
We present mathematical details of several cosmological models, whereby the topological and the geometrical background will be emphasized.
New types "extended" (super)conformal algebras $G^{(\frac n2)}$ are presented. (Su\-per)twistor spaces $T$ are subspaces in cosets $G^{(\frac n2)}/H$. The (super)twistor correspondence has a cleary defined geometrical meaning.
We consider composition and division algebras over the real numbers: We note two r\^oles for the group $G_{2}$: as automorphism group of the octonions and as the isotropy group of a generic 3-form in 7 dimensions. We show why they are…
We give a method to obtain new 7-dimensional Lie algebras endowed with closed and coclosed G2-structures starting from 6-dimensional Lie algebras with symplectic half- at SU(3)-structures and half- at SU(3)- structures, respectively.…
Necessary and sufficient conditions for some deformation algebras to provide formal Frobenius structures are given. Also, examples of formal Frobenius structures with fundamental tensor that is not of the deformation type and examples of…
An algebraic deformation theory of coalgebra morphisms is constructed.
These notes are loosely based on an introductory course in algebraic geometry given at Rutgers University in Spring of 2024. We introduce some relatively advanced topics at the expense of the technical details.
These informal notes are concerned with spaces of functions in various situations, including continuous functions on topological spaces, holomorphic functions of one or more complex variables, and so on.
In this paper we consider the classification of minimal cellular structures of spaces of topological complexity two under some hypotheses on there graded cohomological algebra. This continues the method used by M.Grant et al. in [1].
We give a general account of family algebras over a finitely presented linear operad, this operad together with its presentation naturally defining an algebraic structure on the set of parameters.
This paper is the third in a series of papers, the aim of which is to construct algebraic geometry over metabelian Lie algebras.
We define notions of generically and coarsely computable relations and structures and functions between structures. We investigate the existence and uniqueness of equivalence structures in the context of these definitions
Some notions of algebraic geometry can be defined for arbitrary varieties of algebras. This leads to universal algebraic geometry. The main idea of the presented theory is to consider interactions between algebra, logic and geometry in…
We define algebraic structures on graph cohomology and prove that they correspond to algebraic structures on the cohomology of the spaces of imbeddings of S^1 or R into R^n. As a corollary, we deduce the existence of an infinite number of…
We obtain structure results for locally conformally symplectic Lie algebras. We classify locally conformally symplectic structures on four-dimensional Lie algebras and construct locally conformally symplectic structures on compact quotients…
An expository approach is given on the relationship between algebraic and geometric approaches to properties of isometries in the plane and the 2-sphere.
We study the algebraic and geometric properties of the integral closure of different rings of functions on a real algebraic variety : the regular functions and the continuous rational functions.
In this paper we introduce arrow algebras, simple algebraic structures which induce elementary toposes through the tripos-to-topos construction. This includes localic toposes as well as various realizability toposes, in particular, those…
Geometrization of physical theories have always played an important role in their analysis and development. In this contribution we discuss various aspects concerning the geometrization of physical theories: from classical mechanics to…
Many combinatorial problems can be formulated as a polynomial optimization problem that can be solved by state-of-the-art methods in real algebraic geometry. In this paper we explain many important methods from real algebraic geometry, we…