Infinite Nodal Noncommutative Jordan Algebras; Differentiably Simple Algebras
نویسندگان
چکیده
منابع مشابه
Differentiably Simple Algebras
In this note we announce a result which gives a complete determination of the differentiably simple algebras (in terms of the simple algebras), together with some related results and applications. At the present stage of the theory the algebras considered are for the most part assumed to be finite-dimensional, but otherwise are completely arbitrary (unless expressly stated), i.e. not necessaril...
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1 Background and Motivation We start with an example of affine Kac-Moody algebras and the Virasoro algebra. In this talk, F will be a field with characteristic 0, and all the vector spaces are assumed over F. Denote by Z the ring of integers and by N the set of nonnegative integers. Let 2 ≤ n ∈ N. Set sl(n,F) = {A ∈ Mn×n(F) | tr A = 0}, (1.1) 〈A,B〉 = tr AB for A,B ∈ sl(n,F), (1.2) where Mn×n(F)...
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and x y denotes the product x ‘3~ = my + y.2’. In Section 1 we show that a noncommutative Jordan algebra of characteristic # 2 must satisfy (1). Since power-associative algebras satisfying (1) need not be flexible [5] it follows that the class of power-associative algebras satisfying (1) is strictly larger than the class of noncommutative Jordan algebras. In Section 2 we obtain a structure theo...
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Let E/k be a cubic field extension and J a simple exceptional Jordan algebra of degree 3 over k. Then £ is a reducing field of J if and only if E is isomorphic to a (maximal) subfield of some isotope of /. If k has characteristic not 2 or 3 and contains the third roots of unity then every simple exceptional Jordan division algebra of degree 3 over k contains a cyclic cubic subfield. Exceptional...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1971
ISSN: 0002-9947
DOI: 10.2307/1995618