Special Lie algebras

Abstract

CONTENTS Introduction §1. Structure of special Lie algebras 1.1. Structure of finitely generated special Lie algebras 1.2. Almost soluble Lie algebras 1.3. Semisimple SPI-algebras 1.4. Artinian and Noetherian special Lie algebras 1.5. Relatively free SPI-algebras 1.6. The inheritance problem §2. Envelopes of SPI-algebras 2.1. Universal enveloping algebras 2.2. PI-envelopes of finite-dimensional Lie algebras 2.3. The adjoint algebra 2.4. The Grassmann envelope §3. Special varieties of Lie algebras 3.1. Identities in special algebras 3.2. Identities in finite-dimensional Lie algebras 3.3. Basic and injective rank 3.4. Operations on special varieties §4. Identities and finiteness conditions 4.1. The maximal condition and the Hopf property 4.2. Residual finiteness and representability References