Quadratic (Exceptional) Jordan Algebra of Dimension 54
نویسندگان
چکیده
منابع مشابه
Cubic Rings and the Exceptional Jordan Algebra
In a previous paper [EG] we described an integral structure (J, E) on the exceptional Jordan algebra of Hermitian 3 × 3 matrices over the Cayley octonions. Here we use modular forms and Niemeier’s classification of even unimodular lattices of rank 24 to further investigate J and the integral, even lattice J0 = (ZE) in J . Specifically, we study ring embeddings of totally real cubic rings A into...
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Let # be the exceptional 27-dimensional Jordan algebra over C. Its automorphism group is the Lie group F4(@) and this group is known to have a finite subgroup AL, where A is a self centralizing elementary abelian of order 27, L g SL(3, 3), and L normalizes A. As an A-module, 2 decomposes into a direct sum of l-dimensional spaces jrwhich afford the 27 distinct linear characters x E A n := Hom(A,...
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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: Afyon Kocatepe University Journal of Sciences and Engineering
سال: 2018
ISSN: 2147-5296,2149-3367
DOI: 10.5578/fmbd.66855