Jordan- and Lie geometries

Wolfgang Bertram

Archivum Mathematicum (2013)

  • Volume: 049, Issue: 5, page 275-293
  • ISSN: 0044-8753

Abstract

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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, resp. of a Lie group, with the one of a projective geometry. The text is designed for readers having basic knowledge of Lie theory – we give complete definitions and explain the results by presenting examples, such as Grassmannian geometries.

How to cite

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Bertram, Wolfgang. "Jordan- and Lie geometries." Archivum Mathematicum 049.5 (2013): 275-293. <http://eudml.org/doc/260798>.

@article{Bertram2013,
abstract = {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, resp. of a Lie group, with the one of a projective geometry. The text is designed for readers having basic knowledge of Lie theory – we give complete definitions and explain the results by presenting examples, such as Grassmannian geometries.},
author = {Bertram, Wolfgang},
journal = {Archivum Mathematicum},
keywords = {Jordan algebra (triple system; pair); associative algebra (triple systems; pair); Lie algebra (triple system); graded Lie algebra; symmetric space; torsor (heap; groud; principal homogeneous space); homotopy and isotopy; Grassmannian; generalized projective geometry; Jordan algebra (triple system, pair); associative algebra (triple systems, pair); Lie algebra (triple system); graded Lie algebra; symmetric space; torsor (heap, groud, principal homogeneous space); homotopy and isotopy; Grassmannian; generalized projective geometry},
language = {eng},
number = {5},
pages = {275-293},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Jordan- and Lie geometries},
url = {http://eudml.org/doc/260798},
volume = {049},
year = {2013},
}

TY - JOUR
AU - Bertram, Wolfgang
TI - Jordan- and Lie geometries
JO - Archivum Mathematicum
PY - 2013
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 049
IS - 5
SP - 275
EP - 293
AB - 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, resp. of a Lie group, with the one of a projective geometry. The text is designed for readers having basic knowledge of Lie theory – we give complete definitions and explain the results by presenting examples, such as Grassmannian geometries.
LA - eng
KW - Jordan algebra (triple system; pair); associative algebra (triple systems; pair); Lie algebra (triple system); graded Lie algebra; symmetric space; torsor (heap; groud; principal homogeneous space); homotopy and isotopy; Grassmannian; generalized projective geometry; Jordan algebra (triple system, pair); associative algebra (triple systems, pair); Lie algebra (triple system); graded Lie algebra; symmetric space; torsor (heap, groud, principal homogeneous space); homotopy and isotopy; Grassmannian; generalized projective geometry
UR - http://eudml.org/doc/260798
ER -

References

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