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Automorphism groups of affine varieties and a characterization of affine n-space

Kraft, Hanspeter. (2017) Automorphism groups of affine varieties and a characterization of affine n-space. Tranactions of the Moscow Mathematical Society, 78 (2). pp. 171-186.

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Official URL: https://edoc.unibas.ch/64709/

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Abstract

We show that the automorphism group of affine  -space determines up to isomorphism: If  is a connected affine variety such that as ind-groups, then as varieties. We also show that every torus appears as for a suitable irreducible affine variety  , but that cannot be isomorphic to a semisimple group. In fact, if is finite-dimensional and if , then the connected component is a torus. Concerning the structure of we prove that any homomorphism of ind-groups either factors through where is the Jacobian determinant, or it is a closed immersion. For we show that every nontrivial homomorphism is a closed immersion. Finally, we prove that every nontrivial homomorphism is an automorphism, and that  is given by conjugation with an element from .
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Ehemalige Einheiten Mathematik & Informatik > Algebra (Kraft)
05 Faculty of Science > Departement Mathematik und Informatik > Mathematik
UniBasel Contributors:Kraft, Hanspeter
Item Type:Article, refereed
Article Subtype:Research Article
Publisher:American Mathematical Society
ISSN:0077-1554
e-ISSN:1547-738X
Note:Publication type according to Uni Basel Research Database: Journal article
Language:English
Identification Number:
Last Modified:24 Aug 2018 06:48
Deposited On:24 Aug 2018 06:48

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