Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Constructing $G$-algebras   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 $\mathbb{C}[V]$, it
is shown how one constructs a sequence of projective varieties $\mathbf{V}_k$
such that each point of $\mathbf{V}_k$ 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.

33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
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The categories of this paper are: eess
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int