Noncommutative algebras, context-free grammars and algebraic Hilbert series

2018/07/13 by Roberto La Scala, La Scala, Roberto, Dmitri Piontkovski +3
Mathematics · #05A15 #16E05 #68Q42 #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA #msc:05A15 #msc:16E05 #msc:68Q42

paper · pdf · doi:10.48550/arxiv.1807.05143

26 pages, to appear in Journal of Symbolic Computation

openalex publication_date 2018/07/13 · arxiv created 2019/06/03 · arxiv updated 2019/06/04 · openalex created_date 2022/08/04 · openalex updated_date 2026/07/28

Abstract

In this paper we introduce a class of noncommutative (finitely generated) monomial algebras whose Hilbert series are algebraic functions. We use the concept of graded homology and the theory of unambiguous context-free grammars for this purpose. We also provide examples of finitely presented graded algebras whose corresponding leading monomial algebras belong to the proposed class and hence possess algebraic Hilbert series.

Related

• Graded algebras with prescribed Hilbert series
• Graded Algebras, Algebraic Functions, Planar Trees, and Elliptic Integrals
• Multigraded Hilbert Series of noncommutative modules
• Rationality of Hilbert series in noncommutative invariant theory
• Noncommutatively Graded Algebras