Products of Quasi-Involutions in Unitary Groups
Tóm tắt
Given a regular –-hermitian form on an n-dimensional vector space V over a commutative field K of characteristic ≠ 2 (
$$n \in \mathbb{N} $$
). Call an element σ of the unitary group a quasi-involution if σ is a product of commuting quasi-symmetries (a quasi-symmetry is a unitary transformation with a regular (n−1)-dimensional fixed space). In the special case of an orthogonal group every quasi-involution is an involution. Result: every unitary element is a product of five quasi-involutions. If K is algebraically closed then three quasi-involutions suffice.
Tài liệu tham khảo
Ellers, E. W.: Bireflectionality in classical groups, Canad. J. Math. 29 (1977), 1157–1162.
Huppert, B.: Angewandte lineare Algebra, De Gruyter, Berlin New York, 1990.
Knüppel, F.: Products of involutions in orthogonal groups, Ann. Discr. Math. 37 (1988), 231–248.