Journal article

Publication year: 2019

Pages: 237-275

Journal: Journal of Algebra

Volume number: 520

ISSN: 0021-8693

eISSN: 1090-266X

Open access status: Bronze

DOI Link: https://doi.org/10.1016/j.jalgebra.2018.11.015

Publisher: Elsevier

Abstract: 
Let q: V -> K be the form of degree 4 and H the alternating bilinear form that together give rise to a Freudenthal triple system when the characteristic of K is different from 2 and 3. We give a form Theta of degree 4 on a central cover of V over an arbitrary field in arbitrary characteristic and determine the group of similitudes of Theta. This group coincides with the intersection of the group of similitudes of q and the isometry group of H when the characteristic is different from 2 and 3 and has the expected structure of a suitable Levi subgroup in general. We extend known results about the stabilizers of elements of V and orbits of the group of similitudes and show, in particular, the existence of an exotic set of orbits when char(K) = 2 and K is not perfect. (C) 2018 Elsevier Inc. All rights reserved.

Harvard Citation style: Muehlherr, B. and Weiss, R. (2019) Freudenthal triple systems in arbitrary characteristic, Journal of Algebra, 520, pp. 237-275. https://doi.org/10.1016/j.jalgebra.2018.11.015

APA Citation style: Muehlherr, B., & Weiss, R. (2019). Freudenthal triple systems in arbitrary characteristic. Journal of Algebra. 520, 237-275. https://doi.org/10.1016/j.jalgebra.2018.11.015