Groups Generated by Symplectic Transvections over Local Rings
نویسندگان
چکیده
منابع مشابه
Orbits of Groups Generated by Transvections over F2
Let V be a finite dimensional vector space over the two element field. We compute orbits for the linear action of groups generated by transvections with respect to a certain class of bilinear forms on V . In particular, we compute orbits that are in bijection with connected components of real double Bruhat cells in semisimple groups, extending results of M. Gekhtman, B. Shapiro, M. Shapiro, A. ...
متن کاملSpecial linear groups generated by transvections and embedded projective spaces
We give a characterization of the ‘special linear groups’ T (Ψ,W ) as linear groups generated by a non-degenerate class Σ of abstract root groups such that the elements of A ∈ Σ are transvections.
متن کاملOrthogonal Groups over Local Rings
In an earlier paper [S] we have determined the structure of the linear groups over a local ring. In this note we continue the study of the classical groups over a local ring with the investigation of the orthogonal groups. Our main result (cf. Theorem 6 below) is a complete description of the invariant subgroups of an orthogonal group of noncompact type (i.e., of index ^ 1) over a local ring L ...
متن کاملOrbits under Symplectic Transvections Ii: the Case
Let V be a not necessarily regular, finite-dimensional symplectic space (with symplectic form . ) over a field K where K\rad(|/) is non-empty. Our previous paper [27] (hereinafter referred to as [I]) began the study of the orbits of K\rad(K) under the action of the group Tv{S) of isometries which are products of transvections from a subset S of V. Let G(S) be the graph with vertex set 5 and an ...
متن کاملLow Dimensional Homology of Linear Groups over Hensel Local Rings
We prove that if R is a Hensel local ring with infinite residue field k, the natural map Hi(GLn(R),Z/p) → Hi(GLn(k), Z/p) is an isomorphism for i ≤ 3, p 6= char k. This implies rigidity for Hi(GLn), i ≤ 3, which in turn implies the Friedlander–Milnor conjecture in positive characteristic in degrees ≤ 3. A fundamental question in the homology of linear groups is that of rigidity: given a smooth ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1999
ISSN: 0021-8693
DOI: 10.1006/jabr.1998.7837