Non-noetherian GL-algebras in characteristic two

2024/08/08 by Karthik Ganapathy, Ganapathy, Karthik · 1 citation
Mathematics · #05E40 (Primary) 13E99 #13A50 #14M12 (Secondary) #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2408.04630

openalex publication_date 2024/08/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Over fields of characteristic two, we construct an infinite ascending chain of GL-stable ideals in the coordinate ring of infinite skew-symmetric matrices. This construction provides the first known example of a non-noetherian GL-algebra, thereby resolving a long-standing open question in the area. Our results build on the work of Draisma, Krasilnikov, and Krone.

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• Ideal-theoretic non-noetherianity of polynomial functors in positive characteristic

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