Journalartikel
Autorenliste: Steinbach, AI
Jahr der Veröffentlichung: 1997
Seiten: 281-322
Zeitschrift: Geometriae Dedicata
Bandnummer: 68
Heftnummer: 3
ISSN: 0046-5755
DOI Link: https://doi.org/10.1023/A:1004996924764
Verlag: 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.
Zitierstile
Harvard-Zitierstil: 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-Zitierstil: 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
Schlagwörter
classical group; embedding of projective spaces; fundamental theorem of projective geometry; K-ROOT SUBGROUPS; long root element; OVERGROUPS; Polar space; Siegel transvection; transvection
