2021/06/21 by Diego Aranda-Orna, Aranda-Orna, Diego
Mathematics · #17B70 #17C50 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry and Number Theory #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA) #math.RA #math.RT #msc:17B70 #msc:17C50
paper · pdf · doi:10.48550/arxiv.2106.11373
23 pages
openalex publication_date 2021/06/21 · arxiv created 2022/03/16 · arxiv updated 2022/03/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, the well-known Faulkner construction is revisited and adapted to include the super case, which gives a bijective correspondence between generalized Jordan (super)pairs and faithful Lie (super)algebra (super)modules, under certain constraints (bilinear forms with properties analogous to the ones of a Killing form are required, and only finite-dimensional objects are considered). We always assume that the base field has characteristic different from 2. It is also proven that associated objects in this Faulkner correspondence have isomorphic automorphism group schemes. Finally, this correspondence will be used to transfer the construction of the tensor product to the class of generalized Jordan (super)pairs with "good" bilinear forms.