Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Formulas for primitive Idempotents in Frobenius Algebras and an
  Application to Decomposition maps   In the first part of this paper we present explicit formulas for primitive
idempotents in arbitrary Frobenius algebras using the entries of representing
matrices coming from projective indecomposable modules with respect to a
certain choice of basis. The proofs use a generalisation of the well known
Frobenius-Schur relations for semisimple algebras.
  The second part of this paper considers $\Oh$-free $\Oh$-algebras of finite
$\Oh$-rank over a discrete valuation ring $\Oh$ and their decomposition maps
under modular reduction modulo the maximal ideal of $\Oh$, thereby studying the
modular representation theory of such algebras.
  Using the formulas from the first part we derive general criteria for such a
decomposition map to be an isomorphism that preserves the classes of simple
modules involving explicitly known matrix representations on projective
indecomposable modules.
  Finally we show how this approach could eventually be used to attack a
conjecture by Gordon James in the formulation of Meinolf Geck for
Iwahori-Hecke-Algebras, provided the necessary matrix representations on
projective indecomposable modules could be constructed explicitly.

4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex