This book is directed to researchers in Lie theory and in the theory of linear algebra, associative or otherwise, and to graduate students who have had some background in one or more of these areas.

Table of Contents

• Generalities of finite-dimensional modules
• Behavior upon splitting. Cartan multiplication
• Mappings satisfying symmetric identities
• Structure of symmetric powers
• Construction of representations: Type A and type C (first kind)
• Construction of representations: Type C (second kind)
• Modules for Lie algebras of quadratic forms
• Exceptional types I: \(F_4\) with associative coefficients
• Exceptional types II: Lie algebras coordinatized by octonions
• Exceptional Types III: Relative type \(A_1\)
• Exceptional Types IV: Relative type \(G_2\)
• Appendices: Splitting information
• References