Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Axes of Jordan type in non-commutative algebras   The Peirce decomposition of a Jordan algebra with respect to an idempotent is
well known. This decomposition was taken one step further and generalized
recently by Hall, Rehren and Shpectorov, withtheir introduction of {\it axial
algebras}, and in particular {\it primitive axial algebras of Jordan type} (PJs
for short). It turns out that these notions are closely related to
$3$-transposition groups and vertex operator algebras. De Medts, Peacock,
Shpectorov, and M. Van Couwenberghe generalized axial algebrasto {\it
decomposition algebras} which, in particular, are not necessarily commutative.
This paper deals with decomposition algebras which are non-commutative versions
of PJs.

1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
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The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
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The categories of this paper are: stat
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex