Rational central simple algebras

Zinovy Reichstein; Nikolaus Vonessen

doi:10.1007/BF02761042

Rational central simple algebras

Zinovy Reichstein
, Nikolaus Vonessen

Mathematical Sciences

Oregon State University

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

We introduce a notion of rationality (called toroidal or t-rationality) for central simple algebras which extends Demazure's characterization of rational algebraic varieties via torus actions. We prove a structure theorem for t-rational central simple algebras and study the interplay among t-rationality, crossed products and rationality of the center in the setting of universal division algebras.

Original language	English
Pages (from-to)	253-280
Number of pages	28
Journal	Israel Journal of Mathematics
Volume	95
DOIs	https://doi.org/10.1007/BF02761042
State	Published - 1996

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abstract = "We introduce a notion of rationality (called toroidal or t-rationality) for central simple algebras which extends Demazure's characterization of rational algebraic varieties via torus actions. We prove a structure theorem for t-rational central simple algebras and study the interplay among t-rationality, crossed products and rationality of the center in the setting of universal division algebras.",

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AU - Vonessen, Nikolaus

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AB - We introduce a notion of rationality (called toroidal or t-rationality) for central simple algebras which extends Demazure's characterization of rational algebraic varieties via torus actions. We prove a structure theorem for t-rational central simple algebras and study the interplay among t-rationality, crossed products and rationality of the center in the setting of universal division algebras.

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SN - 0021-2172

VL - 95

SP - 253

EP - 280

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

ER -

Rational central simple algebras

Abstract

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