Jordan 3-graded Lie algebras with polynomial identities
Fernando Montaner, Irene Paniello
TL;DR
This paper investigates Jordan 3-graded Lie algebras satisfying polynomial identities, using the Tits-Kantor-Koecher construction to relate them to Jordan pairs and establish structural theorems.
Contribution
It introduces a Posner-Rowen type theorem for strongly prime PI Jordan 3-graded Lie algebras and describes arbitrary PI Jordan 3-graded Lie algebras via the Kostrikin radical.
Findings
Established an analog of Posner-Rowen theorem for these algebras.
Connected polynomial identities to Jordan pair structures.
Characterized arbitrary PI Jordan 3-graded Lie algebras using the Kostrikin radical.
Abstract
We study Jordan 3-graded Lie algebras satisfying 3-graded polynomial identities. Taking advantage of the Tits-Kantor-Koecher construction, we interpret the PI condition in terms of their associated Jordan pairs, which allows us to formulate an analogous 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.
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Taxonomy
TopicsAdvanced Topics in Algebra · Sphingolipid Metabolism and Signaling · Algebraic structures and combinatorial models