Weakly commensurable groups, with applications to differential geometry

2013/07/04 by Gopal Prasad, Prasad, Gopal, Andrei S. Rapinchuk +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Differential Geometry (math.DG) #FOS: Mathematics #Group Theory (math.GR) #Number Theory (math.NT) #math.DG #math.GR #math.NT

paper · pdf · doi:10.48550/arxiv.1307.1479

Improved exposition, updated bibliography. arXiv admin note: substantial text overlap with arXiv:1212.1217

openalex publication_date 2013/07/04 · arxiv created 2013/11/22 · arxiv updated 2013/11/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The article contains a survey of our results on weakly commensurable arithmetic and general Zariski-dense subgroups, length-commensurable and isospectral locally symmetric spaces and of related problems in the theory of semi-simple agebraic groups. We have included a discussion of very recent results and conjectures on absolutely almost simple algebraic groups having the same maximal tori and finite-dimensional division algebras having the same maximal subfields.

Citations

• Generic elements in Zariski-dense subgroups and isospectral locally symmetric spaces

Related

• Number theoretic techniques in the theory of Lie groups and differential geometry
• Generic elements in Zariski-dense subgroups and isospectral locally symmetric spaces
• Commensurability and representation equivalent arithmetic lattices
• Simple algebraic groups with the same maximal tori, weakly commensurable Zariski-dense subgroups, and good reduction
• Local-global principles for embedding of fields with involution into simple algebras with involution