2008/11/11 by Vitor O. Ferreira, Lucia S. I. Murakami, Ferreira, Vitor O. +1
Materials Science · Mathematics · #16S10 #16W30 #16W50 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Liquid Crystal Research Advancements #Rings and Algebras (math.RA) #math.RA #msc:16S10 #msc:16W30 #msc:16W50
paper · pdf · doi:10.48550/arxiv.0811.1738
7 pages
arxiv created 2008/11/11 · openalex publication_date 2008/11/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
As an instance of a linear action of a Hopf algebra on a free associative algebra, we consider finite group gradings of a free algebra induced by gradings on the space spanned by the free generators. The homogeneous component corresponding to the identity of the group is a free subalgebra which is graded by the usual degree. We look into its Hilbert series and prove that it is a rational function by giving an explicit formula. As an application, we show that, under suitable conditions, this subalgebra is finitely generated if and only if the grading on the base vector space is trivial.