Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Categories of Jordan Structures and Graded Lie Algebras   In the paper we describe the subcategory of the category of Z-graded Lie
algebras which is equivalent to the category of Jordan pairs via a functorial
modification of the TKK construction. For instance, we prove that a Z-graded
Lie algebra can be constructed from a Jordan pair if and only if it is
generated by odd graded components and the second graded homology group is
trivial. Similar descriptions are obtained for Jordan triple systems and Jordan
algebras.

25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex