Jordan 3-graded Lie algebras with polynomial identities

We study Jordan 3-graded Lie algebras satisfying 3-graded polynomial identities. Taking advantage of the Tits-Kantor-Koecher construction, we interpret the PIcondition in terms of their associated Jordan pairs, which allows us to formulate an analogue of Posner-Rowen Theorem for strongly prime PI Jordan 3-graded Lie algebras. Arbitrary PI Jordan 3-graded Lie algebras are also described by introducing the Kostrikin radical of the Lie algebras. (c) 2023 Elsevier B.V. All rights reserved.

Automated summary

In this study, we examine Jordan 3-graded Lie algebras satisfying 3-graded polynomial identities. By utilizing the Tits-Kantor-Koecher construction, we interpret the PI condition in terms of their associated Jordan pairs, thereby formulating an analogue of the Posner-Rowen Theorem for strongly prime PI Jordan 3-graded Lie algebras. Furthermore, we describe arbitrary PI Jordan 3-graded Lie algebras by introducing the Kostrikin radical of the Lie algebras.