Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Duality between $p$-groups with three characteristic subgroups and
  semisimple anti-commutative algebras   Let $p$ be an odd prime and let $G$ be a non-abelian finite $p$-group of
exponent $p^2$ with three distinct characteristic subgroups, namely $1$, $G^p$,
and $G$. The quotient group $G/G^p$ gives rise to an anti-commutative ${\mathbb
F}_p$-algebra $L$ such that the action of ${\rm Aut}(L)$ is irreducible on $L$;
we call such an algebra IAC. This paper establishes a duality $G\leftrightarrow
L$ between such groups and such IAC algebras. We prove that IAC algebras are
semisimple and we classify the simple IAC algebras of dimension at most 4 over
certain fields. We also give other examples of simple IAC algebras, including a
family related to the $m$-th symmetric power of the natural module of ${\rm
SL}(2,{\mathbb F})$.

34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin