#lie-algebras

17. Non-Associative Rings and Algebras

This volume studies algebraic systems where associativity does not hold in general. It includes Lie algebras, Jordan algebras, alternative algebras, and related structures. These systems arise naturally in geometry, physics, and symmetry theory. Part I. Foundations Chapter 1. Non-Associative Structures 1.1 Definitions and examples 1.2 Binary operations without associativity 1.3 Identities and laws 1.4 Homomorphisms 1.5 Subalgebras and quotients Chapter 2. Basic Identities 2.1 Associator and commutator 2.2 Flexible and...