2026/02/28 by Luis Pedro Castellanos Moscoso
Mathematics · #math.DG #msc:53C30 #msc:53D05 #msc:22E25
Revised version. An error in the complex case concerning the possible ranks has been corrected, leading to corresponding modifications to the main classification theorem and related proofs. Numerous typographical errors have also been corrected, and the exposition has been substantially improved. The overall approach and structure of the classification remain unchanged
arxiv created 2026/07/29 · arxiv updated 2026/07/30
We obtain necessary and sufficient conditions to determine the existence of presymplectic forms of a given rank on all almost abelian Lie algebras. We also study the moduli space of presymplectic forms (this is the set of all closed 2-forms of a given rank under a certain natural equivalence relation) on almost abelian Lie algebras. Most importantly we show that for any almost abelian Lie algebra its moduli space of symplectic forms is finite. Moreover we show that up to such natural equivalence all symplectic forms are permutations of a canonical 2-form. The important step in the proof is obtaining canonical representatives for a certain congruence of matrices, which is of some interest for matrix theory on its own.