On regular Lie algebras

Abstract

We study so called regular Lie algebras, i.e., Lie algebras in which each nonzero element is regular. We make a connection with an open problem whether any element of reduced trace zero in a simple associative algebra is a commutator.

Keywords:

• Regular element
• anisotropic Lie algebra
• commutator
• division algebra
• minimal non-abelian Lie algebra

2020 Mathematics Subject Classification::

• 17B05
• 17B50
• 17B60
• 16K20
• 16U99

Acknowledgement

Thanks are due to Alexander Gein and Vicente Varea for supplying me with a hard-to-find item [11].