𝔖 Bobbio Scriptorium
✦   LIBER   ✦

An explicit example of a noncrossed product division algebra

✍ Scribed by Timo Hanke

Publisher
John Wiley and Sons
Year
2004
Tongue
English
Weight
246 KB
Volume
271
Category
Article
ISSN
0025-584X

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

The paper presents an explicit example of a noncrossed product division algebra of index and exponent 8 over the field β„š(s)(t). It is an iterated twisted function field in two variables D(x, Οƒ)(y, Ο„ ) over a quaternion division algebra D which is defined over the number field β„š(√3,βˆšβˆ’7). The automorphisms Οƒ and Ο„ are computed by solving relative norm equations in extensions of number fields. The example is explicit in the sense that its structure constants are known. Moreover, it is pointed out that the same arguments also yield another example, this time over the field β„š((s))((t)), given by an iterated twisted Laurent series ring D((x, Οƒ))((y, Ο„ )) over the same quaternion division algebra D. (Β© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

πŸ“œ SIMILAR VOLUMES

Intercellular adhesion molecule 1 and Ξ²2
Intercellular adhesion molecule 1 and Ξ²2 integrins in C1q-stimulated superoxide production by human neutrophils: An example of a general regulatory mechanism governing acute inflammation
✍ Shivraj Tyagi; Anne Nicholson-Weller; Sergei F. Barbashov; Sander W. Tas; Lloyd πŸ“‚ Article πŸ“… 2000 πŸ› John Wiley and Sons 🌐 English βš– 178 KB

## Objective: To investigate the role of intercellular adhesion molecule 1 (icam-1) and beta2 integrins in the production of superoxide (o2-) by c1q-stimulated human polymorphonuclear leukocytes (pmn). ## Methods: Pmn were pretreated with f(ab')2 fragments of monoclonal antibodies (mab) that bloc