-orthograded quasimonocomposition algebras with one-dimensional null component.
-ортоградуированные монокомпозиционные алгебры.
0-dialgebras with bar-unity and nonassociative Rota--Baxter algebras.
1, 2, 4, 8,... What comes next?
A -grading on a -dimensional simple structurable algebra and related fine gradings on the simple Lie algebras of type
We describe two constructions of a certain -grading on the so-called Brown algebra (a simple structurable algebra of dimension and skew-dimension ) over an algebraically closed field of characteristic different from . The Weyl group of this grading is computed. We also show how this grading gives rise to several interesting fine gradings on exceptional simple Lie algebras of types , and .
A characterization of isoparametric hypersurfaces of Clifford type.
A class of fermionic Novikov superalgebras which is a class of Novikov superalgebras
We construct a special class of fermionic Novikov superalgebras from linear functions. We show that they are Novikov superalgebras. Then we give a complete classification of them, among which there are some non-associative examples. This method leads to several new examples which have not been described in the literature.
A Class of Nonassociative Algebras with Involution Containing the Class of Jordan Algebras.
A concrete analysis of the radical concept.
A construction for algebras satisfying the maximal condition for subalgebras
A general approach to finite-dimensional division algebras
We present a short and rather self-contained introduction to the theory of finite-dimensional division algebras, setting out from the basic definitions and leading up to recent results and current directions of research. In Sections 2-3 we develop the general theory over an arbitrary ground field k, with emphasis on the trichotomy of fields imposed by the dimensions in which a division algebra exists, the groupoid structure of the level subcategories 𝒟ₙ(k), and the role played by the irreducible...
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.
A Künneth Formula for the Cyclic Cohomology of Z/2-Graded Algebras.
A Leibniz algebra structure on the second tensor power.
A new approach to Hom-left-symmetric bialgebras
The main purpose of this paper is to consider a new definition of Hom-left-symmetric bialgebra. The coboundary Hom-left-symmetric bialgebra is also studied. In particular, we give a necessary and sufficient condition that -matrix is a solution of the Hom--equation by a cocycle condition.
A non-abelian tensor product of Leibniz algebra
Leibniz algebras are a non-commutative version of usual Lie algebras. We introduce a notion of (pre)crossed Leibniz algebra which is a simultaneous generalization of notions of representation and two-sided ideal of a Leibniz algebra. We construct the Leibniz algebra of biderivations on crossed Leibniz algebras and we define a non-abelian tensor product of Leibniz algebras. These two notions are adjoint to each other. A (co)homological characterization of these new algebraic objects enables us to...
A non-semiprime associative algebra with zero weak radical.
The weak radical, W-Rad(A) of a non-associative algebra A, has been introduced by A. Rodríguez Palacios in [3] in order to generalize the Johnson's uniqueness of norm theorem to general complete normed non-associative algebras (see also [2] for another application of this notion). In [4], he showed that if A is a semiprime non-associative algebra with DCC on ideals, then W-Rad(A) = 0. In the first part of this paper we give an example of a non-semiprime associative algebra A with DCC on ideals and...
A note on commutativity of nonassociative rings.
A note on the number of generators of a nodal algebra