Products of involutions in \(O^ +(V)\)

DOI10.1016/0024-3795(87)90092-9zbMath0623.20036OpenAlexW2003625272MaRDI QIDQ1091474

Klaus Nielsen, Frieder Knüppel

Publication date: 1987

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0024-3795(87)90092-9

zbMATH Keywords

special orthogonal grouporthogonal decompositionsymmetric bilinear formproduct of involutionsorthogonally indecomposable \(\pi \)- modules

Mathematics Subject Classification ID

Factorization of matrices (15A23) Generators, relations, and presentations of groups (20F05) Quadratic and bilinear forms, inner products (15A63) Other matrix groups over fields (20H20) Orthogonal and unitary groups in metric geometry (51F25)

Related Items (12)

Decomposition of complex hyperbolic isometries by involutions ⋮ Every real symplectic matrix is a product of real symplectic involutions ⋮ Reversible quaternionic hyperbolic isometries ⋮ Commutator groups of orthogonal groups over the reals with emphasis on Lorentz groups. ⋮ Factoring formal maps into reversible or involutive factors. ⋮ Expressing infinite matrices as products of involutions ⋮ Reality of unipotent elements in classical Lie groups ⋮ Reversible complex hyperbolic isometries ⋮ Conjugacy classes in Möbius groups ⋮ Reality properties of conjugacy classes in algebraic groups. ⋮ 5-reflectionality of anisotropic orthogonal groups over valuation rings ⋮ Conjugacy classes of involutions in the Lorentz group \(\Omega(V)\) and in \(\text{SO}(V)\)

Cites Work

• On bireflectionality and trireflectionality of orthogonal groups
• Product of two involutions
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