TY - JOUR

T1 - Strongly non-degenerate lie algebras

AU - Perera, Francesc

AU - Molina, Mercedes Siles

PY - 2008/12/1

Y1 - 2008/12/1

N2 - 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.

AB - 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.

U2 - https://doi.org/10.1090/S0002-9939-08-09558-0

DO - https://doi.org/10.1090/S0002-9939-08-09558-0

M3 - Article

VL - 136

SP - 4115

EP - 4124

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

ER -