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Products of symmetries in unitary groups
Publikationstyp
Journal Article
Date Issued
1997-07-15
Sprache
English
Author(s)
TORE-URI
Volume
260
Issue
1-3
Start Page
9
End Page
42
Citation
Linear Algebra and Its Applications 1-3 (260): 9-42 (1997-07-15)
Publisher DOI
Scopus ID
Publisher
American Elsevier Publ.
Given a regular --hermitian form on a finite-dimensional vector space V over a commutative field K of characteristic ≠ 2 such that the norm on K is surjective onto the fixed field of - (this is true whenever K is finite). Call an element σ of the unitary group a symmetry if σ2 = 1 and the negative space of σ is 1-dimensional. If π is unitary and det π ∈ 1, -1, we prove that π is a product of symmetries (with a few exceptions when K = GF 9 and dim V = 2) and we find the minimal number of factors in such a product.
DDC Class
004: Informatik
510: Mathematik