On free associative algebras linearly graded by finite groups

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dc.creatorFerreira, Vitor O.
dc.creatorMurakami, Lucia S. I.
dc.date2008-11-11
dc.date.accessioned2026-07-07T10:17:30Z
dc.date.available2026-07-07T10:17:30Z
dc.descriptionAs 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.
dc.description7 pages
dc.identifierhttps://arxiv.org/abs/0811.1738
dc.identifierhttp://arxiv.org/abs/0811.1738
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/173872
dc.subjectRings and Algebras
dc.subject16S10; 16W30; 16W50
dc.titleOn free associative algebras linearly graded by finite groups
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