Journal of Lie Theory

no. 2
Associative Geometries. I: Torsors, Linear Relations and Grassmannians
Journal of Lie Theory, Volume 20 (2010) no. 2, pp. 215-252
We define and investigate a geometric object, called an "associative geometry", corresponding to an associative algebra (and, more generally, to an associative pair). Associative geometries combine aspects of Lie groups and of generalized projective geometries, where the former correspond to the Lie product of an associative algebra and the latter to its Jordan product. A further development of the theory encompassing involutive associative algebras will be given in Part II of this work.
DOI: 10.5802/jolt.594
Classification: 20N10, 17C37, 16W10
Keywords: Associative algebras and pairs, torsor, heap, groud, principal homogeneous space, semitorsor, linear relations, homotopy, isotopy, Grassmannian, generalized projective geometry 
@article{JOLT_2010_20_2_a0,
     author = {W. Bertram and M. Kinyon},
     title = {Associative {Geometries.} {I:} {Torsors,} {Linear} {Relations} and {Grassmannians}},
     journal = {Journal of Lie Theory},
     pages = {215--252},
     year = {2010},
     volume = {20},
     number = {2},
     doi = {10.5802/jolt.594},
     zbl = {1206.20074},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.594/}
}
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W. Bertram; M. Kinyon. Associative Geometries. I: Torsors, Linear Relations and Grassmannians. Journal of Lie Theory, Volume 20 (2010) no. 2, pp. 215-252. doi: 10.5802/jolt.594

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