Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $\cal N$-Extension of duble-graded supersymmetric and superconformal
  quantum mechanics   In the recent paper, Bruce and Duplij introduced a double-graded version of
supersymmetric quantum mechanics (SQM). It is an extension of Lie
superalgebraic nature of ${\cal N}=1$ SQM to a $\mathbb{Z}_2^2$-graded
superalgebra. In this work, we propose an extension of Bruce-Duplij model to
higher values of $\cal N.$ Furthermore, it is shown that our construction of
double-graded SQM is a special case of the method which converts a given Lie
superalgebra to a $\mathbb{Z}_2^2$-graded superalgebra. By employing this
method one may convert a model of superconformal mechanics to its double-graded
version. The simplest example of ${\cal N}=1$ double-graded superconformal
mechanics is studied in some detail.

9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga