Journal article
Authors list: Steinbach, AI
Publication year: 1997
Pages: 281-322
Journal: Geometriae Dedicata
Volume number: 68
Issue number: 3
ISSN: 0046-5755
DOI Link: https://doi.org/10.1023/A:1004996924764
Publisher: Springer
Abstract:
We are concerned with finite-dimensional classical groups over arbitrary commutative fields. In an orthogonal group a Siegel transvection, that is, an element centralizing l(perpendicular to) for some totally singular 2-dimensional subspace l, plays the same role as a transvection in the linear, symplectic or unitary groups. The Main Theorem of this paper describes the possible embeddings of classical groups in classical groups such that (Siegel) transvections act as (Siegel) transvections.
Citation Styles
Harvard Citation style: Steinbach, A. (1997) Subgroups of classical groups generated by transvections or Siegel transvections I: Embeddings in linear groups, Geometriae Dedicata, 68(3), pp. 281-322. https://doi.org/10.1023/A:1004996924764
APA Citation style: Steinbach, A. (1997). Subgroups of classical groups generated by transvections or Siegel transvections I: Embeddings in linear groups. Geometriae Dedicata. 68(3), 281-322. https://doi.org/10.1023/A:1004996924764
Keywords
classical group; embedding of projective spaces; fundamental theorem of projective geometry; K-ROOT SUBGROUPS; long root element; OVERGROUPS; Polar space; Siegel transvection; transvection
