User menu

Accès à distance ? S'identifier sur le proxy UCLouvain

Division algebras of degree 4 and 8 with involution

Primary tabs

Amitsur, Shimshon A. [Hebrew University of Jerusalem] Rowen, Louis H. [Bar-Ilan University] Tignol, Jean-Pierre [UCL]

We develop necessary and sufficient conditions for central simple algebras to have involutions of the first kind, and to be tensor products of quaternion subalgebras. The theory is then applied to give an example of a division algebra of degree 8 with involution (of the first kind), without quaternion subalgebras, answering an old question of Albert; another example is a division algebra of degree 4 with involution (*) has no (*)-invariant quaternion subalgebras.

Document type Article de périodique (Journal article) – Article de recherche
Access type Accès restreint
Publication date 1979
Language Anglais
Journal information "Israel Journal of Mathematics" - Vol. 33, no. 2, p. 133-148 (1979)
Peer reviewed yes
Publisher Magnes Press ((Israel) Jerusalem)
issn 0021-2172
e-issn 1565-8511
Publication status Publié
Affiliations Hebrew University of Jerusalem - Department of Mathematics
Bar-Ilan University - Department of Mathematics
UCL - SC/MATH - Département de mathématique
Links
  1. A. A. Albert,Structure of Algebras, Amer. Math. Soc. Colloq. Publ.24, Providence, R.I., 1961.
  2. S. A. Amitsur and D. Saltman,Generic abelian crossed products, J. Algebra51 (1978), 76–87.
  3. L. Rowen,Some results on the center of a ring with polynomial identity, Bull. Amer. Math. Soc.79(1973), 219–223.
  4. L. Rowen,Central simple algebras, Israel J. Math.29(1978), 285–301.
  5. J. Tignol,Sur les classes de similitude de corps a involution de degré 8, C. R. Acad. Sci. ParisA286 (1978), 875–876.
  6. J. Tignol, Decomposition et descente de produits tensoriels d’algebres de quaternions, Rapport Sem. Math. Pure UCL76 (1978).
Bibliographic reference Amitsur, Shimshon A. ; Rowen, Louis H. ; Tignol, Jean-Pierre. Division algebras of degree 4 and 8 with involution. In: Israel Journal of Mathematics, Vol. 33, no. 2, p. 133-148 (1979)
Permanent URL http://hdl.handle.net/2078.1/110639