منابع مشابه
Jordan- and Lie Geometries
In these lecture notes we report on research aiming at understanding the relation beween algebras and geometries, by focusing on the classes of Jordan algebraic and of associative structures and comparing them with Lie structures. The geometric object sought for, called a generalized projective, resp. an associative geometry, can be seen as a combination of the structure of a symmetric space, r...
متن کاملJordan Geometries by Inversions
Jordan geometries are defined as spaces X equipped with point reflections Jxz a depending on triples of points (x, a, z), exchanging x and z and fixing a. In a similar way, symmetric spaces have been defined by Loos ([Lo69]) as spaces equipped with point reflections Sx fixing x, and therefore the theories of Jordan geometries and of symmetric spaces are closely related to each other – in order ...
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 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: Archivum Mathematicum
سال: 2013
ISSN: 0044-8753,1212-5059
DOI: 10.5817/am2013-5-275