Related papers: Exceptional symmetric domains
Let S be a smooth algebraic surface satisfying the following property: H^i(\oc_S(C))=0 (i=1,2) for any irreducible and reduced curve C of S. The aim of this paper is to provide a characterization of special linear systems on S which are…
Locally finiteness of some varieties of nonassociative coalgebras is studied and the Gelfand-Dorfman construction for Novikov coalgebras and the Kantor construction for Jordan super-coalgebras are given. We give examples of a non-locally…
We define Jordan quadruple systems by the polynomial identities of degrees 4 and 7 satisfied by the Jordan tetrad {a,b,c,d} = abcd + dcba as a quadrilinear operation on associative algebras. We find further identities in degree 10 which are…
This is an introduction to advanced linear algebra, with emphasis on geometric aspects, and with some applications included too. We first review basic linear algebra, notably with the spectral theorem in its general form, and with the…
The paper is devoted to the description of the varieties of complex 5-dimensional nilpotent Jordan superalgebras. We find all representatives for the isomorphism classes, using the Jordan normal form, results of simultaneous matrix…
The group of automorphisms of the Kac Jordan superalgebra is described, and used to classify the maximal subalgebras.
A construction of the magic square, and hence of exceptional Lie algebras, is carried out using trialities rather than division algebras. By way of preparation, a comprehensive discussion of trialities is given, incorporating a number of…
We show that the there exists an algebraic rate of convergence of solutions of finite-difference approximations for uniformly elliptic Isaacs in smooth bounded domains.
In this paper we address the celebrated Albert problem for exceptional Jordan algebras (i.e. Albert algebras): Does every Albert division algebra contain a cubic cyclic subfield? We prove that for any Albert division algebra $A$ over a…
We study the exponential map of connected symmetric spaces and characterize, in terms of midpoints and of infinitesimal conditions, when it is a diffeomorphism, generalizing the Dixmier-Saito theorem for solvable Lie groups. We then give a…
These notes consist of a study of special Lagrangian submanifolds of Calabi-Yau manifolds and their moduli spaces. The particular case of three dimensions, important in string theory, allows us to introduce the notion of gerbes. These offer…
We construct and classify all possible Magic Squares (MS's) related to Euclidean or Lorentzian rank-3 simple Jordan algebras, both on normed division algebras and split composition algebras. Besides the known Freudenthal-Rozenfeld-Tits MS,…
For a Jordan domain with sufficiently smooth boundaries, the solution to the Dirichlet problem for second order skew-symmetric strongly elliptic system with constant coefficients and regular enough boundary data is constructed in the form…
A previous article was devoted to an analysis of the symmetry properties of a class of first-order delay ordinary differential systems (DODSs). Here we concentrate on linear DODSs. They have infinite-dimensional Lie point symmetry groups…
We prove the existence of nontrivial unbounded exceptional domains in the Euclidean space $\R^N$, $N\geq4$. These domains arise as perturbations of complements of straight cylinders in $\R^N$, and by definition they support a positive…
The classification, up to isomorphism, of two-dimensional (not necessarily commutative) Jordan algebras over algebraically closed fields and $\mathbb{R}$ is presented in terms of their matrices of structure constants.
A notion of duality of weight systems which corresponds to Batyrev's toric mirror symmetry is given. Explicit duality on the (1,1)-cohomology of K3 surfaces which are minimal models of toric hypersurfaces is constructed using monomial…
Building on the established theories of Jordan triple disystems and Leibniz triple systems, we introduce and develop the theory of associative triple trisystems, filling a significant gap in the existing framework. We establish the…
We put forward a definition for spectral triples and algebraic backgrounds based on Jordan coordinate algebras. We also propose natural and gauge-invariant bosonic configuration spaces of fluctuated Dirac operators and compute them for…
We prove a number of double-sided estimates relating discrete counterparts of several classical conformal invariants of a quadrilateral: cross-ratios, extremal lengths and random walk partition functions. The results hold true for any…