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Geometry of 2 × 2 hermitian matrices.
- Source :
- Science in China. Series A: Mathematics, Physics & Astronomy; Aug2002, Vol. 45 Issue 8, p1025-1037, 13p
- Publication Year :
- 2002
-
Abstract
- Let D be a division ring which possesses an involution a → α . Assume that $$F = \{ a \in D|a = \overline a \} $$ is a proper subfield of D and is contained in the center of D. It is pointed out that if D is of characteristic not two, D is either a separable quadratic extension of F or a division ring of generalized quaternions over F and that if D is of characteristic two, D is a separable quadratic extension of F. Thus the trace map Tr: D → F, a → a + a is always surjective, which is formerly posed as an assumption in the fundamental theorem of n×n hermitian matrices over D when n ≥ 3 and now can be deleted. When D is a field, the fundamental theorem of 2 × 2 hermitian matrices over D has already been proved. This paper proves the fundamental theorem of 2×2 hermitian matrices over any division ring of generalized quaternions of characteristic not two [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10069283
- Volume :
- 45
- Issue :
- 8
- Database :
- Complementary Index
- Journal :
- Science in China. Series A: Mathematics, Physics & Astronomy
- Publication Type :
- Academic Journal
- Accession number :
- 49372448
- Full Text :
- https://doi.org/10.1007/BF02879986