منابع مشابه
Finitary Lie algebras
An algebra is called finitary if it consists of finite-rank transformations of a vector space. We classify finitary simple and finitary irreducible Lie algebras over an algebraically closed field of characteristic 6= 2, 3.
متن کاملCohomology of Jordan triples and Lie algebras
We develop a cohomology theory for Jordan triples, including the infinite dimensional ones, by means of the cohomology of TKK Lie algebras. This enables us to apply Lie cohomological results to the setting of Jordan triples.
متن کاملConvolution over Lie and Jordan algebras
Given a ternary relation C on a set U and an algebra A, we present a construction of a convolution algebra A(U,C) of U = (U,C) over A. This generalises bothmatrix algebras and algebras obtained from convolution of monoids. To any class of algebras corresponds a class of convolution structures. Our study cases are the classes of commutative, associative, Lie, and Jordan algebras. In each of thes...
متن کاملGraded Lie Algebras Defined by Jordan Algebras and Their Representations
In this talk we introduce the notion of a generalized representation of a Jordan algebra with unit which has the following properties: 1) Usual representations and Jacobson representations correspond to special cases of generalized representations. 2) Every simple Jordan algebra has infinitely many nonequivalent generalized representations. 3) There is a one-to-one correspondence between irredu...
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: Journal of Algebra
سال: 2004
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2004.06.013