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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, II

Linked Tori, II

(p.47) Chapter Six Linked Tori, II
Descent in Buildings (AM-190)

Bernhard M¨uhlherr

Holger P. Petersson

Richard M. Weiss

Princeton University Press

This chapter proves several more results about weak isomorphisms between Moufang sets arising from quadratic forms and involutory sets. It first fixes a non-trivial anisotropic quadratic space Λ‎ = (K, L, q) before considering two proper anisotropic pseudo-quadratic spaces. It then describes a quaternion division algebra and its standard involution, a second quaternion division algebra and its standard involution, and an involutory set with a quaternion division algebra and its standard involution. It concludes with one more small observation regarding a pointed anisotropic quadratic space and shows that there is a unique multiplication on L that turns L into an integral domain with a multiplicative identity.

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

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