Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Membership deformation of commutativity and obscure $n$-ary algebras   A general mechanism for "breaking" commutativity in algebras is proposed: if
the underlying set is taken to be not a crisp set, but rather an obscure/fuzzy
set, the membership function, reflecting the degree of truth that an element
belongs to the set, can be incorporated into the commutation relations. The
special "deformations" of commutativity and $\varepsilon $-commutativity are
introduced in such a way that equal degrees of truth result in the
"nondeformed" case. We also sketch how to "deform" $\varepsilon$-Lie algebras
and Weyl algebras. Further, the above constructions are extended to $n$-ary
algebras for which the projective representations and $\varepsilon
$-commutativity are studied.

17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph