Applying Group Theory Philosophy to Leibniz Algebras: Some New Developments

Abstract

This survey is an attempt of describing of main contours of a recently developing general theory of Leibniz Algebras. This theory based on the employing of methods and approaches which are proved to be exceedingly effective in infinite group theory. The survey addresses a number of natural problems that quite often have analogs in other disciplines, discusses the parts of the theory that have been already developed, and argues which parts of it should be developed further.

Keywords

• leibniz algebra
• lie algebra
• ideal
• finitely dimensional leibniz algebra
• locally nilpotent and nilpotent leibniz algebra