The Hilbert series of the preprojective algebras

2024/02/24 by Hiroyuki Minamoto, Minamoto, Hiroyuki
Mathematics · #Advanced Topics in Algebra #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2402.15732

openalex publication_date 2024/02/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The aim of this short note is to prove the formula of the Hilbert series of the preprojective algebras in arbitrary characteristic by making effective use of the formulas of the Hilbert series of differential graded (dg) algebras with Adams grading. We also compute the Hilbert series of the quiver Heisenberg algebras, a special class of central extensions of preprojective algebras.

Related

• Koszulity and the Hilbert series of preprojective algebras
• Quiver Heisenberg algebras: a cubic analogue of preprojective algebras
• Graded algebras with prescribed Hilbert series
• Sets of Hilbert series and their applications
• The Hilbert series of algebras of Veronese type