-orthograded quasimonocomposition algebras with one-dimensional null component.
-ортоградуированные монокомпозиционные алгебры.
A generalisation of Amitsur's A-polynomials
We find examples of polynomials whose eigenring is a central simple algebra over the field .
A group of a Lie algebra.
About relationship between generalized structurable algebras and Lie related triples.
Automorphisms and pseudo-automorphisms of extra algebras
Division algebras that generalize Dickson semifields
We generalize Knuth’s construction of Case I semifields quadratic over a weak nucleus, also known as generalized Dickson semifields, by doubling of central simple algebras. We thus obtain division algebras of dimension by doubling central division algebras of degree . Results on isomorphisms and automorphisms of these algebras are obtained in certain cases.
Edomorphisms and Null subalgeras of finite dimensional algebras.
Existentially closed Leibniz algebras and an embedding theorem
In this paper we introduce the notion of existentially closed Leibniz algebras. Then we use HNN-extensions of Leibniz algebras in order to prove an embedding theorem.
Invariant theory of G2 and Spin7.
Invariants of Lie color algebras acting on graded algebras
We prove a series of "going-up" theorems contrasting the structure of semiprime algebras and their subalgebras of invariants under the actions of Lie color algebras.
Non-Associative Division Algebras Admitting Many Derivations.
n-лиевы алгебры.
Octonionic Cayley spinors and
Attempts to extend our previous work using the octonions to describe fundamental particles lead naturally to the consideration of a particular real, noncompact form of the exceptional Lie group , and of its subgroups. We are therefore led to a description of in terms of octonionic matrices, generalizing previous results in the case. Our treatment naturally includes a description of several important subgroups of , notably , , and (the double cover of) . An interpretation of the actions...
On automorphism groups of non-associative Boolean rings.
On generalized Jordan derivations of Lie triple systems
Under some conditions we prove that every generalized Jordan triple derivation on a Lie triple system is a generalized derivation. Specially, we conclude that every Jordan triple -derivation on a Lie triple system is a -derivation.
On regular and extremely regular algebras
On the classification of the real flexible division algebras
We investigate the class of finite-dimensional real flexible division algebras. We classify the commutative division algebras, completing an approach by Althoen and Kugler. We solve the isomorphism problem for scalar isotopes of quadratic division algebras, and classify the generalised pseudo-octonion algebras. In view of earlier results by Benkart, Britten and Osborn and Cuenca Mira et al., this reduces the problem of classifying the real flexible division algebras to the normal...
On the structure of Jordan *-derivations
Operads of decorated trees and their duals
This is an extended version of a talk presented by the second author on the Third Mile High Conference on Nonassociative Mathematics (August 2013, Denver, CO). The purpose of this paper is twofold. First, we would like to review the technique developed in a series of papers for various classes of di-algebras and show how the same ideas work for tri-algebras. Second, we present a general approach to the definition of pre- and post-algebras which turns out to be equivalent to the construction of dendriform...