Categories of Jordan Structures and Graded Lie Algebras

Details Categories of Jordan Structures and Graded Lie Algebras Categories of Jordan Structures and Graded Lie Algebras

2011-06-13

arxiv.org/abs/1106.2447v1

Mathematics

Rings and Algebras

Scientific paper

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.

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