Jordan structures and non associative geometry

Wolfgang Bertram

Description

Niveau: Supérieur, Doctorat, Bac+8
Jordan structures and non-associative geometry Wolfgang Bertram Institut Elie Cartan, Universite Nancy I, Faculte des Sciences, B.P. 239, 54506 Vandœuvre-les-Nancy, Cedex, France Abstract. We give an overview over constructions of geometries associated to Jor- dan structures (algebras, triple systems and pairs), featuring analogs of these con- structions with the Lie functor on the one hand and with the approach of non- commutative geometry on the other hand. Keywords: Jordan pair, Lie triple system, graded Lie algebra, filtered Lie alge- bra, generalized projective geometry, flag geometries, (non-) associative algebra and geometry AMS subject classification: 17C37, 17B70, 53C15 Introduction Let us compare two aspects of the vast mathematical topic “links between ge- ometry and algebra”: on the one hand, the Lie functor establishes a close rela- tion between Lie groups (geometric side) and Lie algebras (algebraic side); this is generalized by a correspondence between symmetric spaces and Lie triple systems (see [Lo69]). On the other hand, the philosophy of Non-Commutative Geometry generalizes the relation between usual, geometric point-spaces M (e.g., manifolds) and the commutative and associative algebra Reg(M,K) of “regular” (e.

• reg


• algebra


• lie triple


• associative geometry


• geometric space


• banach-jordan


• graded lie


• commutative geometry


• purely geometric


• jordan pairs

Sujets

• Bertram
• Cartan
• Álgebra

Informations

• Publié par: profil-zyak-2012
• Nombre de lectures: 47
• Langue: English

Extrait

INSTITUT NATIONAL DE LA STATISTIQUE ET DES ETUDES ECONOMIQUES
Série des Documents de Travail du CREST
(Centre de Recherche en Economie et Statistique)










n° 2007-25

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* I am grateful above all to my Ph. D. advisor Philippe Jehiel for his continuous support. I would like to thank
seminar participants in Paris-PSE and Vienna ESEM 2006 Conference. All errors are mine.
1 Laboratoire d’Economie Industrielle, CREST-INSEE, 28 Rue des Saints-Pères, 75007 PARIS, France.
[e-mail] ∗
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