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Article
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Transactions of the American Mathematical Society
Article . 1967 . Peer-reviewed
Data sources: Crossref
Transactions of the American Mathematical Society
Article . 1967 . Peer-reviewed
Data sources: Crossref
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On a Class of Nodal Noncommutative Jordan Algebras

On a class of nodal noncommutative Jordan algebras
Authors: Goldman, Jerry I.;

On a Class of Nodal Noncommutative Jordan Algebras

Abstract

where f-g is the product of f=f(x1, . . ., xn) and g=g(x1, . . ., xn) in Bn and the = 1[xi, xj] = (xixj -xjxi) are arbitrary except for the proviso that at least one of them is nonsingular. That is, there must exist a cij = aij1 + wij with aij =0. This implies that n ? 2. The class K was constructed by L. Kokoris who proved [2], [3] that every simple nodal noncommutative Jordan algebra is in K. He also proved that not all the algebras of the class K are simple. Two papers have appeared which were concerned with studying derivations of some of the algebras in K. The first of these by R. Schafer [7] described derivation algebras for the cases cij in F and n =2 and demonstrated relationships between certain ideals of these algebras and types of simple Lie algebras of characteristic p. He made use of two properties which were later generalized by R. Oehmke, namely that the algebras in K for the cases cij in F and n =2 are Lie-admissible and that, for n = 2, the generators xl and x2 could be chosen so that c12 = 1 + axp -1*x2-1 for a in F. In his paper [4], Oehmke determined the derivation algebras of all simple Lieadmissible algebras A of K. He proved that generators could be chosen for these A which satisfy a useful Lie-multiplication table, which is a generalization of

Keywords

Noncommutative Jordan algebras, nodal noncommutative Jordan algebras, Oehmke multiplication table, simplicity, Lie admissibility

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
4
Average
Top 10%
Average
bronze