Reduction theory for stably graded Lie algebras

2024/05/16 by Jack A. Thorne, Thorne, Jack A. · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2405.10217

openalex publication_date 2024/05/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define a reduction covariant for the representations a la Vinberg associated to stably graded Lie algebras. We then give an analogue of the LLL algorithm for the odd split special orthogonal group and show how this can be combined with our theory to effectively reduce the coefficients of vectors in a representation connected to 2-descent for odd hyperelliptic curves.

Cited by

• Lower bounds on heights of odd degree points of hyperelliptic curves

Related

• Families of curves in Vinberg representations
• Diagonal reduction algebras of \gl type
• The Levi Decomposition of a Graded Lie Algebra
• Constructing Graded Lie Algebras
• On some classes of Z-graded Lie algebras