Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Modular representation theory and commutative Banach algebras   In a recent paper of Benson and Symonds, a new invariant was introduced for
modular representations of a finite group. An interpretation was given as a
spectral radius with respect to a Banach algebra completion of the
representation ring. Our purpose here is to take these notions further, and
investigate the structure of the resulting Banach algebras. Some of the
material in that paper is repeated here in greater generality, and for clarity
of exposition.
  We give an axiomatic definition of an abstract representation ring, and
representation ideal. The completion is then a commutative Banach algebra, and
the techniques of Gelfand from the 1940s are applied in order to study the
space of algebra homomorphisms to $\mathbb C$. One surprising consequence of
this investigation is that the Jacobson radical and the nil radical of a
(complexified) representation ring always coincide.
  These notes are intended for representation theorists. So background material
on commutative Banach algebras is given in detail, whereas representation
theoretic background is more condensed.

30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn