Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Semi-Associative $3$-Algebras   A new 3-ary non-associative algebra, which is called a semi-associative
$3$-algebra, is introduced, and the double modules and double extensions by
cocycles are provided. Every semi-associative $3$-algebra $(A, \{ , , \})$ has
an adjacent 3-Lie algebra $(A, [ , , ]_c)$. From a semi-associative $3$-algebra
$(A, \{, , \})$, a double module $(\phi, \psi, M)$ and a cocycle $\theta$, a
semi-direct product semi-associative $3$-algebra $A\ltimes_{\phi\psi} M $ and a
double extension $(A\dot+A^*, \{ , , \}_{\theta})$ are constructed, and
structures are studied.

27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th