Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gorenstein simplices and the associated finite abelian groups   It is known that a lattice simplex of dimension $d$ corresponds a finite
abelian subgroup of $(\mathbb{R}/\mathbb{Z})^{d+1}$. Conversely, given a finite
abelian subgroup of $(\mathbb{R}/\mathbb{Z})^{d+1}$ such that the sum of all
entries of each element is an integer, we can obtain a lattice simplex of
dimension $d$. In this paper, we discuss a characterization of Gorenstein
simplices in terms of the associated finite abelian groups. In particular, we
present complete characterizations of Gorenstein simplices whose normalized
volume equals $p,p^2$ and $pq$, where $p$ and $q$ are prime numbers with $p
\neq q$. Moreover, we compute the volume of the dual simplices of Gorenstein
simplices.

28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat