Related papers: Jordan algebras over algebraic varieties

For any positive integer $n$, $n$-derived-simple derived discrete algebras are classified up to derived equivalence. Furthermore, the Jordan-H\"older theorems for all kinds of derived categories of derived discrete algebras are obtained.

In this paper, we classify four-dimensional Jordan algebras over an algebraically closed field of characteristic different of two. We establish the list of 73 non-isomorphic Jordan algebras.

These notes were written following lectures I had the pleasure of giving on this subject at Keio University, during November and December 2004. The first part is about new applications of Jordan algebras to the geometry of Hermitian…

Let $k$ be an arbitrary field. The main aim of this paper is to prove the Tits-Weiss conjecture for Albert division algebras over $k$ which are pure first Tits constructions. This conjecture asserts that for an Albert division algebra $A$…

We show that primitive 4-generated axial algebras of Jordan type are at most 81-dimensional.

We consider finite dimensional Jordan superalgebras $\jor$ over an algebraically closed field of characteristic 0, with solvable radical $\rad$ such that $\radd=0$ and $\jor/\rad$ is a simple Jordan superalgebra of one of the following…

Assuming a particular case of Borisov--Alexeev--Borisov conjecture, we prove that finite subgroups of the automorphism group of a finitely generated field over Q have bounded orders. Further, we investigate which algebraic varieties have…

In this paper, we study the variety $Jor_{3}$ of three-dimensional Jordan algebras over the field of real numbers. We establish the list of $26$ non-isomorphic Jordan algebras and describe the irreducible components of $Jor_{3}$ proving…

Jordan, Wigner and von Neumann classified the possible algebras of quantum mechanical observables, and found they fell into 4 "ordinary" families, plus one remarkable outlier: the exceptional Jordan algebra. We point out an intriguing…

The purpose of this paper is a partial progress towards classification of simple infinite dimensional Jordan superalgebras. First, we prove that the only simple infinite dimensional Jordan superalgebras with finite dimensional even parts…

In this paper, we develop a method to obtain the algebraic classification of noncommutative Jordan algebras from the classification of Jordan algebras of the same dimension. We use this method to obtain the algebraic classification of…

We consider Artinian algebras $A$ over a field $\mathsf{k}$, both graded and local algebras. The Lefschetz properties of graded Artinian algebras have been long studied, but more recently the Jordan type invariant of a pair $(\ell,A)$ where…

The Matsuo algebra associated with a connected Fischer space is shown to be a Jordan algebra over a field of characteristic 3 if and only if the Fischer space is isomorphic to either the affine space of order 3 or the Fischer space…

This work provides a unified formalism for studying difference and (Hasse-) differential algebraic geometry, by introducing a theory of "iterative Hasse rings and schemes". As an application, Hasse jet spaces are constructed generally,…

We give the presentation of exceptional bounded symmetric domains using the Albert algebra and exceptional Jordan triple systems. The first chapter is devoted to Cayley-Graves algebras, the second to exceptional Jordan triple systems. In…

Recently, an algebraic generalization of the Jordan-Wigner transformation was introduced and applied to one- and two-dimensional systems. This transformation is composed of the interactions $\eta_{i}$ that appear in the Hamiltonian ${\cal…

We give a uniform construction of the finite simple groups $E_6(q)$, $F_4(q)$ and ${}^2E_6(q)$, which does not require any special treatment for characteristics 2 or 3, and in particular avoids any mention of quadratic Jordan algebras.…

To an arbitrary Lie superalgebra $L$ we associate its Jordan double ${\mathcal Jor}(L)$, which is a Jordan superalgebra. This notion was introduced by the second author before. Now we study further applications of this construction. First,…

We prove a semisimplicity criterion for a large class of algebras by a new method. This can be applied to Brauer, BMW, and $q$-Brauer algebras.

In this article we begin the study of representations of simple finite-dimensional noncommutative Jordan superalgebras. In the case of degree $\geq 3$ we show that any finite-dimensional representation is completely reducible and, depending…