K₁-Stability of symplectic modules over monoid algebras

2025/04/28 by Rabeya Basu, Basu, Rabeya, Maria Ann Mathew +1
Computer Science · Mathematics · #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #K-Theory and Homology (math.KT) #Polynomial and algebraic computation #Rings and Algebras (math.RA) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2504.19492

openalex publication_date 2025/04/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let R be a regular ring of dimension d and L be a c-divisible monoid. If K₁Sp(R) is trivial and k ≥ d+2, then we prove that the symplectic group Sp_2k(R[L]) is generated by elementary symplectic matrices over R[L]. When d ≤ 1 or R is a geometrically regular ring containing a field, then improved bounds have been established. We also discuss the linear case, extending the work of Gubeladze.

Citations

• Symplectic K-theory and a problem of Murthy
• Unimodular rows over monoid extensions of overrings of polynomial rings
• Unimodular rows over monoid rings
• Injective Stability for K₁ of Classical Modules
• Local-Global Principle for Transvection Groups
• Polytopes, Rings, and K-Theory
• Euler class group of Laurent polynomial ring : local case

Related

• Symplectic K-theory and a problem of Murthy
• Injective Stability for K₁ of Classical Modules
• Improved injective stability for relative K₁Sp-groups
• Equality of Linear and Symplectic Orbits
• The Stable Symplectic category and a conjecture of Kontsevich