A-Transvections and Witt's Theorem in Symplectic A-Modules

作者：Ntumba Patrice P^*; Anyaegbunam Adaeze C

来源：Mediterranean Journal of Mathematics, 2011, 8(4): 509-524.

DOI：10.1007/s00009-010-0102-8

• A-homothecy
• A-hyperplane
• A-transvection
• A-transvection of classical type
• transvection matrix
• symplectic A-module
• PID-algebra sheaf
• orthogonally convenient pairing

Building on prior joint work by Mallios and Ntumba, we study transvections (J. Dieudonne), 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).

• 出版日期2011-12