Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The universality of one half in commutative nonassociative algebras with
  identities   In this paper we will explain an interesting phenomenon which occurs in
general nonassociative algebras. More precisely, we establish that any
finite-dimensional commutative nonassociative algebra over a field satisfying
an identity always contains $\frac12$ in its Peirce spectrum. We also show that
the corresponding $\frac12$-Peirce module satisfies the Jordan type fusion
laws. The present approach is based on an explicit representation of the Peirce
polynomial for an arbitrary algebra identity. To work with fusion rules, we
develop the concept of the Peirce symbol and show that it can be explicitly
determined for a wide class of algebras. We also illustrate our approach by
further applications to genetic algebras and algebra of minimal cones (the
so-called Hsiang algebras).

14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ