Nonassociative algebras: a framework for differential geometry.
Nonassociative algebras with submultiplicative bilinear form.
Non-Associative Division Algebras Admitting Many Derivations.
Nonassociative ultraprime normed algebras.
Recently M. Mathieu [9] has proved that any associative ultraprime normed complex algebra is centrally closed. The aim of this note is to announce the general nonassociative extension of Mathieu's result obtained by the authors [2].
Nonassociativity in VOA theory and finite group theory
We discuss some examples of nonassociative algebras which occur in VOA (vertex operator algebra) theory and finite group theory. Methods of VOA theory and finite group theory provide a lot of nonassociative algebras to study. Ideas from nonassociative algebra theory could be useful to group theorists and VOA theorists.
Noncommutative Jordan algebras containing minimal inner ideals
Nondegenerate invariant bilinear forms on nonassociative algebras.
Novikov superalgebras with
Novikov superalgebras are related to quadratic conformal superalgebras which correspond to the Hamiltonian pairs and play a fundamental role in completely integrable systems. In this note we show that the Novikov superalgebras with and are of type and give a class of Novikov superalgebras of type with .
n-лиевы алгебры.
Octonion multiplication and Heawood’s map
In this note, the octonion multiplication table is recovered from a regular tesselation of the equilateral two timensional torus by seven hexagons, also known as Heawood’s map.
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 a class of non-associative rings
On Algebraic Power-Associative and Jordan Algebras with Semi-Normal Functionals.
On Algebras all of Whose Subalgebras are Simple; Some Solutions of Plonka's Problem
On automorphism groups of non-associative Boolean rings.
On free subgroups of units in quaternion algebras
It is well known that for the ring H(ℤ) of integral quaternions the unit group U(H(ℤ) is finite. On the other hand, for the rational quaternion algebra H(ℚ), its unit group is infinite and even contains a nontrivial free subgroup. In this note (see Theorem 1.5 and Corollary 2.6) we find all intermediate rings ℤ ⊂ A ⊆ ℚ such that the group of units U(H(A)) of quaternions over A contains a nontrivial free subgroup. In each case we indicate such a subgroup explicitly. We do our best to keep the arguments...
On free subgroups of units in quaternion algebras II
Let A ⊆ ℚ be any subring. We extend our earlier results on unit groups of the standard quaternion algebra H(A) to units of certain rings of generalized quaternions H(A,a,b) = ((-a,-b)/A), where a,b ∈ A. Next we show that there is an algebra embedding of the ring H(A,a,b) into the algebra of standard Cayley numbers over A. Using this embedding we answer a question asked in the first part of this paper.
On generalized formal power series
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 Herstein's theorems relating modularity in A and A(+).
In this paper we will examine the relationship between modularity in the lattices of subalgebras of A and A(+), for A an associative algebra over an algebraically closed field. To this aim we will construct an ideal which measures the modularity of an algebra (not necessarily associative) in paragraph 1, examine modular associative algebras in paragraph 2, and prove in paragraph 3 that the ideal constructed in paragraph 1 coincides for A and A(+). We will also examine some properties of the ideal...