Lie superautomorphisms on associative algebras

Yuri Bahturin, Matej Brešar
2009 Proceedings of the American Mathematical Society  
The results on Lie homomorphisms of associative algebras are extended to certain associative superalgebras. It is shown that under appropriate conditions a Lie superautomorphism of A = A 0 ⊕ A 1 is a sum of a superautomorphism or the negative of a superantiautomorphism and a central map. In particular we consider the situation when A is a central simple algebra and its Z 2 -grading is induced by an idempotent.
doi:10.1090/s0002-9939-09-10136-3 fatcat:ysn7eitrwretnohtggr423cio4