6 citations · 13 across the 19 of their papers we have counts for
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Frobenius forms on weakly primitive axial algebras of Jordan type
Louis Rowen, Yoav Segev
In a previous paper we studied ``weakly primitive axial algebras'' with respect to more general fusion rules, for which at least one axis satisfies the fusion rules. In this contin…
Two axes in non-commutative algebras with a Frobenius form
Yoav Segev
Throughout this paper is a commutative non-associative algebra over a field of characteristic not In addition posses a Frobenius form. We obtain detailed…
Weakly primitive axial algebras
Louis Halle Rowen, Yoav Segev
In earlier work we studied the structure of primitive axial algebras of Jordan type (PAJ's), not necessarily commutative, in terms of their primitive axes. In this paper we weaken…
Primitive 4-generated axial algebras of Jordan type
Tom De Medts, Louis Rowen, Yoav Segev
We show that primitive 4-generated axial algebras of Jordan type are at most 81-dimensional.
Structure of primitive axial algebras
Louis Halle Rowen, Yoav Segev
"Fusion rules" are laws of multiplication among eigenspaces of an idempotent. This terminology is relatively new and is closely related to primitive axial algebras, introduced rece…
A uniform characterization of the octonions and the quaternions using commutators
Erwin Kleinfeld, Yoav Segev
Let be a ring with which is not commutative. Assume that a non-zero commutator in is not a zero divisor. Assume further that either is alternative, but not as…
Axes in non-associative algebras
Louis Rowen, Yoav Segev
"Fusion rules" are laws of multiplication among eigenspaces of an idempotent. This terminology is relatively new and is closely related to axial algebras, introduced recently by Ha…
Axes of Jordan type in non-commutative algebras
Louis Rowen, Yoav Segev
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…
Alternative rings whose associators are not zero-divisors
Erwin Kleinfeld, Yoav Segev
The purpose of this short note is to prove that if is an alternative ring whose associators are not zero-divisors, then has no zero divisors. By a result of Bruck and Klein…
A short characterization of the Octonions
Erwin Kleinfeld, Yoav Segev
In this paper we prove that if is a proper alternative ring whose additive group has no -torsion and whose non-zero commutators are not zero-divisors, then has no zero-d…
Flexible idempotents in nonassociative algebras
Louis Rowen, Yoav Segev
``Fusion rules'' are laws of multiplication among eigenspaces of an idempotent. We establish fusion rules for flexible power-associative algebras, following Albert. We define the n…
Half-axes in power associative algebras
Yoav Segev
Let be a commutative, non-associative algebra over a field of characteristic . A half-axis in is an idempotent such that satisfies the Peir…
Associative and Jordan algebras generated by two idempotents
Louis Rowen, Yoav Segev
Associative or Jordan algebras generated by two idempotents are described precisely.
On graphs and valuations
Ido Efrat, Andrei S. Rapinchuk, Yoav Segev
In the last two decades new techniques emerged to construct valuations on an infinite division ring given a normal subgroup of finite index. These techniques we…
On finite homomorphic images of the multiplicative group of a division algebra
Yoav Segev
This paper, together with a forthcoming paper by the author and Seitz, proves the Margulis-Platonov conjecture concerning the normal subgroup structure of algebraic groups over num…