Constructing G-algebras

2016/05/30 by De Laet, Kevin
#16W20 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1605.09265

Abstract

In this article we define G-algebras, that is, graded algebras on which a reductive group G acts as gradation preserving automorphisms. Starting from a finite dimensional G-module V and the polynomial ring ℂ[V], it is shown how one constructs a sequence of projective varieties V_k such that each point of V_k corresponds to a graded algebra with the same decomposition up to degree k as a G-module. After some general theory, we apply this to the case that V is the n+1-dimensional permutation representation of S_n+1, the permutation group on n+1 letters.

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