Cyclic compositions and trisotopies
- 关键词：Cyclic compositions ; Composition algebras ; Cubic norm structures ; Tits process
- 刊名：Journal of Algebra
- 出版年：2007
- 期刊代码：69_00218693
- 类别：mt
- 出版时间：1 January 2007
- 卷：307
- 期：1
- 页码：49-96
- 文件大小：371 K
摘要
Cyclic compositions in the sense of Springer [T.A. Springer, Oktaven, Jordan-Algebren und Ausnahmegruppen, Universität Göttingen, 1963] and Knus, Merkurjev, Rost and Tignol [M.-A. Knus, A. Merkurjev, M. Rost, J.-P. Tignol, The Book of Involutions, Amer. Math. Soc. Colloq. Publ., vol. 44, Amer. Math. Soc., Providence, RI, 1998. With a preface in French by J. Tits] are investigated by means of cyclic trisotopies, a concept originally due to Albert [A.A. Albert, A construction of exceptional Jordan division algebras, Ann. of Math. (2) 67 (1958) 1–28]. Using the quadrupling of composition algebras, we enumerate cyclic trisotopies and compositions in a rational manner, i.e., without extending the base field. We relate cyclic trisotopies explicitly to simple associative algebras of degree 3 with involution and to the Tits process of cubic Jordan algebras.