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...
متن کاملThe exceptional Jordan algebra and the matrix string
ABSTRACT A new matrix model is described, based on the exceptional Jordan algebra, J3 O . The action is cubic, as in matrix Chern-Simons theory. We describe a compactification that, we argue, reproduces, at the one loop level, an octonionic compactification of the matrix string theory in which SO(8) is broken to G2. There are 27 matrix degrees of freedom, which under Spin(8) transform as the ve...
متن کاملA Moufang Loop, the Exceptional Jordan Algebra, and a Cubic Form in 27 Variables
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,...
متن کاملA Note on the Jordan Canonical Form
A proof of the Jordan canonical form, suitable for a first course in linear algebra, is given. The proof includes the uniqueness of the number and sizes of the Jordan blocks. The value of the customary procedure for finding the block generators is also questioned. 2000 MSC: 15A21. The Jordan form of linear transformations is an exceeding useful result in all theoretical considerations regarding...
متن کاملJordan Gradings on Exceptional Simple Lie Algebras
Models of all the gradings on the exceptional simple Lie algebras induced by Jordan subgroups of their groups of automorphisms are provided.
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ژورنال
عنوان ژورنال: Proceedings of the National Academy of Sciences
سال: 1950
ISSN: 0027-8424,1091-6490
DOI: 10.1073/pnas.36.7.372