xiv Contents

Appendix A. 433

§A.1. Background from Lie Theory 433

A.1.1. Root Systems 433

A.1.2. The Weyl Group 434

A.1.3. Reductive Lie Algebras 435

A.1.4. A Theorem of Harish-Chandra 436

§A.2. Hopf Algebras and Z2-Graded Structures 437

A.2.1. Hopf Algebras 437

A.2.2. Remarks on Z2-Graded Structures: The Rule Of

Signs 440

A.2.3. Some Constructions with U(g)-Modules 443

A.2.4. The Supersymmetric and Superexterior Algebras 446

A.2.5. Actions of the Symmetric Group 447

§A.3. Some Ring Theoretic Background 449

A.3.1. The Diamond Lemma 449

A.3.2. Clifford Algebras 452

A.3.3. Ore Extensions 455

§A.4. Exercises 456

Appendix B. 463

Bibliography 471

Index 485