Geometriae Dedicata

, Volume 65, Issue 3, pp 313–321 | Cite as

Products of Quasi-Involutions in Unitary Groups

  • FLORIAN BÜNGER
  • FRIEDER KNÜPPEL

Abstract

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.

unitary groups factorization quasi-involutions. 

References

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    Ellers, E. W.: Bireflectionality in classical groups, Canad. J. Math. 29 (1977), 1157–1162.Google Scholar
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    Huppert, B.: Angewandte lineare Algebra, De Gruyter, Berlin New York, 1990.Google Scholar
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    Knüppel, F.: Products of involutions in orthogonal groups, Ann. Discr. Math. 37 (1988), 231–248.Google Scholar

Copyright information

© Kluwer Academic Publishers 1997

Authors and Affiliations

  • FLORIAN BÜNGER
    • 1
  • FRIEDER KNÜPPEL
    • 1
  1. 1.Mathematisches Seminar derUniversität KielKielGermany

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