Bibliothèque de L'IMIST/CNRST

Includes bibliographical references (p. 849-891) and index.

pt. 1. Protective characters. Chapter 1. An Invitation to projective characters ; Chapter 2. Clifford theory for projective characters ; Chapter 3. Correspondences for projective characters ; Chapter 4. Generalized projective characters ; Chapter 5. Projective character tables -- part 2. Protective representations II. Chapter 6. Splitting fields ; Chapter 7. Projective Schur index ; Chapter 8. Projective representations of Abelian Groups -- part 3. Group-graded algebras. Chapter 9. Graded modules ; Chapter 10. Clifford theory for graded algebras : restriction and induction ; Chapter 11. Clifford theory for graded algebras : extensions of modules ; Chapter 12. Clifford theory for group algebras ; Chapter 13. Graded group rings -- part 4. The Schur index. Chapter 14. Foundations of the theory -- Chapter 15. Main theorems -- Bibliography -- Notation -- Index.

This third volume can be roughly divided into two parts. The first part is devoted to the investigation of various properties of projective characters. Special attention is drawn to spin representations and their character tables and to various correspondences for projective characters. Among other topics, projective Schur index and projective representations of abelian groups are covered. The last topic is investigated by introducing a symplectic geometry on finite abelian groups. The second part is devoted to Clifford theory for graded algebras and its application to the corresponding theory for group algebras. The volume ends with a detailed investigation of the Schur index for ordinary representations. A prominant role is played in the discussion by Brauer groups together with cyclotomic algebras and cyclic algebras.

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