Strongly non-degenerate lie algebras

Francesc Perera, Mercedes Siles Molina

Research output: Contribution to journalArticleResearchpeer-review

4 Citations (Scopus)

Abstract

Let A be a semiprime 2- and 3-torsion free non-commutative associative algebra. We show that the Lie algebra Der(A) of (associative) derivations of A is strongly non-degenerate, which is a strong form of semiprimeness for Lie algebras, under some additional restrictions on the center of A. This result follows from a description of the quadratic annihilator of a general Lie algebra inside appropriate Lie overalgebras. Similar results are obtained for an associative algebra A with involution and the Lie algebra SDer(A) of involution preserving derivations of A. © 2008 American Mathematical Society.
Original languageEnglish
Pages (from-to)4115-4124
JournalProceedings of the American Mathematical Society
Volume136
DOIs
Publication statusPublished - 1 Dec 2008

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