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Descent in Buildings (AM-190)$
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Bernhard Mühlherr, Holger P. Petersson, and Richard M. Weiss

Print publication date: 2015

Print ISBN-13: 9780691166902

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691166902.001.0001

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Linked Tori, I

Linked Tori, I

(p.41) Chapter Five Linked Tori, I
Descent in Buildings (AM-190)

Bernhard M¨uhlherr

Holger P. Petersson

Richard M. Weiss

Princeton University Press

This chapter investigates the consequences of the assumption that one Moufang set is weakly isomorphic to another. It first introduces some well-known facts about involutions which are assembled in a few lemmas, including those dealing with an involutory set, a biquaternion division algebra, and a quaternion division algebra with a standard involution. It then presents a notation for a non-trivial anisotropic quadratic space and another for an involutory set are presented, along with assumptions for a pointed anisotropic quadratic space and the standard involution of a quaternion. It also makes a number of propositions regarding the standard involution of a quaternion and a biquaternion. Results about weak isomorphisms between Moufang sets arising from involutory sets are given.

Keywords:   quaternion division algebra, Moufang set, weak isomorphism, involutory set, biquaternion division algebra, standard involution, anisotropic quadratic space

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