Products of quasireflections and transvections over local rings

DOI10.1007/BF01222386zbMath0639.20031MaRDI QIDQ1100286

Rolfdieter Frank, Erich W. Ellers

Publication date: 1988

Published in: Journal of Geometry (Search for Journal in Brave)

zbMATH Keywords

symplectic groupsupper boundquadratic formorthogonal groupsunitary groupslocal ringsesquilinear formminimal number of factorsfactorization of isometries into reflections, quasireflections, and transvectionsproduct of quasi reflections and transvections

Mathematics Subject Classification ID

Factorization of matrices (15A23) Other matrix groups over rings (20H25) Orthogonal and unitary groups in metric geometry (51F25) Quadratic forms over local rings and fields (11E08)

Related Items (7)

Hjelmslevgruppen mit Nachbar-Homomorphismus. (Hjelmslev groups with neighbour-homomorphism) ⋮ Width of groups of type \(\mathrm E_6\) with respect to root elements. II. ⋮ 5-reflectionality of anisotropic orthogonal groups over valuation rings ⋮ The width of the group \(\mathrm{GL}(6,K)\) with respect to a set of quasiroot elements. ⋮ Projective metric geometry and Clifford algebras ⋮ Generators for classical groups of modules over local rings ⋮ Width of groups of type $\mathrm E_{6}$ with respect to root elements. I

Cites Work

• Factorization of transformations over a local ring
• Decomposition of orthogonal, symplectic, and unitary isometries into simple isometries
• Quadratic forms over semilocal rings
• Eine Zerlegung der unitären Gruppe über lokalen Ringen
• Orthogonale Gruppen Uber Lokalen Ringen
• Generators of Orthogonal Groups over Valuation Rings
• On the Decomposition of Orthogonalities into Symmetries
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