Related papers: Jordan structures and non-associative geometry

We extend the loop algebra construction for algebras graded by abelian groups to study graded-simple algebras over the field of real numbers (or any real closed field). As an application, we classify up to isomorphism the graded-simple…

The Peirce decomposition of a Jordan algebra with respect to an idempotent is well known. This decomposition was taken one step further and generalized recently by Hall, Rehren and Shpectorov, withtheir introduction of {\it axial algebras},…

The non-commutative algebraic analog of the moduli of vector and covector fields is built. The structure of moduli of derivations of non-commutative algebras are studied. The canonical coupling is introduced and the conditions for…

We review Hodge structures, relating filtrations, Galois Theory and Jordan-Holder structures. The prototypical case of periods of Riemann surfaces is compared with the Galois-Artin framework of algebraic numbers.

Poisson algebra is usually defined to be a commutative algebra together with a Lie bracket, and these operations are required to satisfy the Leibniz rule. We describe Poisson structures in terms of a single bilinear operation. This enables…

Let $A$ and $B$ be commutative algebras and $n\geqslant 2$ an integer. Then each $n-$ Jordan homomorphism $h:A\rightarrow B$ is an $n-$homomorphism.

Extending a recently proposed procedure of construction of various elements of diffential geometry on noncommutative algebras, we obtain these structures on noncommutative superalgebras. As an example, a quantum superspace covariant under…

We introduce an algebraic framework for the description of baryons. Within this framework we study a collective string-like model and show that this model gives a good overall description of the presently available data. We discuss in…

In this paper, we classify Jordan superalgebras of dimension up to three over an algebraically closed field of characteristic different of two. Our main motivation to obtain such classification comes out from the intention to give an answer…

A representation of the exceptional Lie algebras is presented. It reflects a simple unifying view and it is realized in terms of Zorn-type matrices. The role of the underlying Jordan pair and Jordan algebra content is crucial in the…

We compute minimal sets of generators for the S_n-modules (n <= 4) of multilinear polynomial identities of arity n satisfied by the Jordan product and the Jordan diproduct (resp. pre-Jordan product) in every triassociative (resp.…

In this paper we prove that any nonlinear Jordan derivation on triangular algebras is an additive derivation. As a byproduct, we obtain that any nonlinear Jordan derivation on nest algebras over infinite dimensional Hilbert spaces is inner.

We give algebraic and geometric classifications of complex $4$-dimensional nilpotent noncommutative Jordan algebras. Specifically, we find that, up to isomorphism, there are only $18$ non-isomorphic nontrivial nilpotent noncommutative…

There exists two types of nonassociative algebras whose associator satisfies a symmetric relation associated with a 1-dimensional invariant vector space with respect to the natural action of the symmetric group on three elements. The first…

In this paper we study the structure of the Algebraic Cobordism ring of a variety as a module over the Lazard ring, and show that it has relations in positive codimensions. We actually prove the stronger graded version. This extends the…

Throughout the papers of E.B. Vinberg some non-abelian gradings of simple Lie algebras were introduced and investigated, namely short $SO_3 -$ and $SL_3$ - structures. We study another kind of them -- short $SL_2$ - structures. The main…

This paper is devoted to the classification of complex pre-Jordan algebras in the sense of isomorphisms in dimensions $\leq$ 3. All Rota-Baxter operators on complex Jordan algebras in dimensions $\leq$ 3 and the induced pre-Jordan algebras…

We study the structures of arbitrary split $\delta$ Jordan-Lie algebras with symmetric root systems. We show that any of such algebras $L$ is of the form $L = U + \sum\limits_{[j] \in \Lambda/\sim}I_{[j]}$ with $U$ a subspace of $H$ and any…

In the article we study the simple unital communitative three-dimensional algebras over an algebraically closed field of characteristic not equal to 2. It is proved that every simple unital communitative three-dimensional algebra of…

We call a linear operator on a vector space over a field Jordanable if it has a Jordan canonical form. An almost Abelian Lie algebra has only one non-vanishing Lie bracket, which is given by a linear operator. If the latter is Jordanable…