On homotopes of Novikov algebras.
On Leibniz algebras with maximal cyclic subalgebras
We begin to study the structure of Leibniz algebras having maximal cyclic subalgebras.
On Lie algebras in braided categories
The category of group-graded modules over an abelian group is a monoidal category. For any bicharacter of this category becomes a braided monoidal category. We define the notion of a Lie algebra in this category generalizing the concepts of Lie super and Lie color algebras. Our Lie algebras have -ary multiplications between various graded components. They possess universal enveloping algebras that are Hopf algebras in the given category. Their biproducts with the group ring are noncommutative...
On Linear and Quadratic Jordan Division Algebras.
On maximal subalgebras of central simple Malcev algebras.
In this paper the structure of the maximal elements of the lattice of subalgebras of central simple non-Lie Malcev algebras is considered. Such maximal subalgebras are studied in two ways: first by using theoretical results concerning Malcev algebras, and second by using the close connection between these simple non-Lie Malcev algebras and the Cayley-Dickson algebras, which have been extensively studied (see [4]).
On Nambu bracket representations of 3-algebras.
On one-sided division infinite-dimensional normed real algebras.
In this note we introduce the concept of Cayley homomorphism which is closely related with those of composition algebra and normalized orthogonal multiplication. The key result shows the existence of certain types of Cayley homomorphisms for infinite dimension. As an application we prove the existence of left division infinite-dimensional complete normed real algebras with left unity.
On positive and critical theories of some classes of rings.
On regular and extremely regular algebras
On rings with alternators in the commutative center
On some anticyclic operads.
On some classes of nilpotent Leibniz algebras.
On Some Generalizations of Lie Algebras
On some properties of the upper central series in Leibniz algebras
This article discusses the Leibniz algebras whose upper hypercenter has finite codimension. It is proved that such an algebra includes a finite dimensional ideal such that the factor-algebra is hypercentral. This result is an extension to the Leibniz algebra of the corresponding result obtained earlier for Lie algebras. It is also analogous to the corresponding results obtained for groups and modules.
On the associative Nijenhuis relation.
On the classification of -dimensional -manifold algebras
-manifold algebras are focused on the algebraic properties of the tangent sheaf of -manifolds. The local classification of 3-dimensional -manifolds has been given in A. Basalaev, C. Hertling (2021). We study the classification of 3-dimensional -manifold algebras over the complex field .
On the classification of 3-dimensional non-associative division algebras over -adic fields
Let be a prime and a -adic field (a finite extension of the field of -adic numbers ). We employ the main results in [12] and the arithmetic of elliptic curves over to reduce the problem of classifying 3-dimensional non-associative division algebras (up to isotopy) over to the classification of ternary cubic forms over (up to equivalence) with no non-trivial zeros over . We give an explicit solution to the latter problem, which we then relate to the reduction type of the jacobian...
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 degenerations of finite dimensional nilpotent complex Leibniz algebras.
On the dimension of a composition algebra.