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.
Deanna M. Caveny < cavenyd@cofc.edu >
Oleg N. Smirnov < smirnov@cofc.edu >