On free associative algebras linearly graded by finite groups - Mathematics > Rings and AlgebrasReport as inadecuate




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Abstract: As an instance of a linear action of a Hopf algebra on a free associativealgebra, we consider finite group gradings of a free algebra induced bygradings on the space spanned by the free generators. The homogeneous componentcorresponding to the identity of the group is a free subalgebra which is gradedby the usual degree. We look into its Hilbert series and prove that it is arational function by giving an explicit formula. As an application, we showthat, under suitable conditions, this subalgebra is finitely generated if andonly if the grading on the base vector space is trivial.



Author: Vitor O. Ferreira, Lucia S. I. Murakami

Source: https://arxiv.org/







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