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Jordan structures and non associative geometry

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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


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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

The Ausubel-Milgrom Proxy
*Auction with Final Discounts

1L. LAMY





























Les documents de travail ne reflètent pas la position de l'INSEE et n'engagent que
leurs auteurs.

Working papers do not reflect the position of INSEE but only the views of the authors.


* 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.
laurent.lamy@ensae.fr ∗



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0,l ∈ S
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→ 0
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While y = 0 do
y := 1
for l = 1 to N do
if Π (a)<πbl l
then πb := max{0,πb −} ; y := 0l l
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