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Singular and Totally Singular Unitary Spaces

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Dolphin, Andrew [UCL]

In this article, we present a decomposition theorem for unitary spaces over a central simple division algebra with involution in characteristic 2. This is a generalization of a decomposition result for quadratic forms in characteristic 2 from [4] and extends a generalization of the Witt decomposition theorem for nonsingular spaces in this setting to cover spaces that may be singular

Document type Article de périodique (Journal article) – Article de recherche
Publication date 2015
Language Anglais
Journal information "Communications in Algebra" - Vol. 43, no.12, p. 5141-5158 (2015)
Peer reviewed yes
Publisher Taylor & Francis Inc. ((United States) Philadelphia)
issn 0092-7872
e-issn 1532-4125
Publication status Publié
Affiliation UCL - SST/ICTM - Institute of Information and Communication Technologies, Electronics and Applied Mathematics
Keywords Central simple algebras ; Characteristic two ; Generalised quadratic forms ; Involutions ; Unitary spaces ; Witt decomposition
Links
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  3. Elomary Mohamed Abdou, Tignol Jean-Pierre, Classification of Quadratic Forms over Skew Fields of Characteristic 2, 10.1006/jabr.2001.8737
  4. Hoffmann Detlev W., Laghribi Ahmed, 10.1090/s0002-9947-04-03461-0
  5. Knus , M.A. ( 1991 ).Quadratic and Hermitian Forms over Rings.Grundlehren der mathematischen Wissenschaften, Vol. 294. Springer-Verlag .
  6. Knus , M.A. Merkurjev , A. S. Rost , M. Tignol , J.P. ( 1998 ).The Book of Involutions.Colloq. Publ., Am. Math. Soc., Vol. 44. Am. Math. Soc .
  7. Laghribi Ahmed, On splitting of totally singular quadratic forms, 10.1007/bf02875725
  8. Pierce Richard S., Associative Algebras, ISBN:9781475701654, 10.1007/978-1-4757-0163-0
  9. Tits J., Formes quadratiques, groupes orthogonaux et alg�bres de Clifford, 10.1007/bf01404536
  10. Wall C. T. C., Compositio Math., 22, 425 (1970)
  11. Witt E., J. Reine Angew. Math., 176, 31 (1936)
Bibliographic reference Dolphin, Andrew. Singular and Totally Singular Unitary Spaces. In: Communications in Algebra, Vol. 43, no.12, p. 5141-5158 (2015)
Permanent URL http://hdl.handle.net/2078.1/173363