Hilbert series of PI relatively free G-graded algebras are rational functions

Eli Aljadeff*, Alexei Kanel-Belov

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

Given a finite group G and a field F of characteristic zero, we let F〈x1,g1,⋯,xr,gr〉 be the free G-graded F-algebra generated by homogeneous variables {x i,gi}gi∈ G. Let ℐ be a G-graded T-ideal of F〈x1,g1,⋯,xr,g r〉 which is PI (that is, the algebra F〈x1,g 1,⋯,xr,gr〉/ℐ is PI). We prove that the Hilbert series of F〈1,g1,⋯,x r,gr〉/ℐ is a rational function. More generally, we show that the Hilbert series which corresponds to any g-homogeneous component of F〈1,g1,⋯,xr,g r〉/ℐ is a rational function.

Original languageEnglish
Pages (from-to)520-532
Number of pages13
JournalBulletin of the London Mathematical Society
Volume44
Issue number3
DOIs
StatePublished - Jun 2012
Externally publishedYes

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