2005/09/23 by Cornel Baetica, C. Baetica, Baetica, C. +2
Mathematics · #16A08 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #Rings and Algebras (math.RA) #Rings, Modules, and Algebras #math.QA #math.RA #msc:16A08
paper · pdf · doi:10.48550/arxiv.math/0509542
12 pages
arxiv created 2005/09/23 · openalex publication_date 2005/09/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this note we relate the valuations of the algebras appearing in the non-commutative geometry of quantized algebras to properties of sub-lattices in some vector spaces. We consider the case of algebras with PBW-bases and prove that under some mild assumptions the valuations of the ground field extend to a non-commutative valuation. Later we introduce the notion of F-reductor and graded reductor and reduce the problem of finding an extending non-commutative valuation to finding a reductor in an associated graded ring having a domain for its reduction.