Abstract:
Building on prior joint work by Mallios and Ntumba, we study
transvections (J. Dieudonn´e), a theme already important from the classical
theory, in the realm of Abstract Geometric Algebra, referring herewith
to symplectic A-modules. A characterization of A-transvections, in terms
of A-hyperplanes (Theorem 1.4), is given together with the associated
matrix definition (Corollary 1.5). By taking the domain of coefficients A
to be a PID-algebra sheaf, we also consider the analogue of a form of the
classical Witt’s extension theorem, concerning A-symplectomorphisms
defined on appropriate Lagrangian sub-A-modules (Theorem 2.3 and
2.4).
