Group Representations

Group Representations

1st Edition - February 18, 1994

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  • Editor: Gregory Karpilovsky
  • eBook ISBN: 9780080872919

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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.

Table of Contents

  • Preface. Part I: Projective Characters. 1. An Invitation to Projective Characters. 2. Clifford Theory for Projective Characters. 3. Correspondence for Projective Characters. 4. Generalized Projective Characters. Projective Character Tables. Part II: Projective Representations II. 6. Splitting Fields. 7. Projective Schur Index. 8. Projective Representations of Abelian Groups. Part III: Group-Graded Algebras. 9. Graded Modules. 10. Clifford Theory for Graded Algebras: Restriction and Induction. 11. Clifford Theory for Graded Algebras: Extensions of Modules. 12. Clifford Theory for Group Algebras. 13. Graded Group Rings. Part IV: The Schur Index. 14. Foundations of the Theory. 15. Main Theorems. Bibliography. Notation. Index.

Product details

  • No. of pages: 906
  • Language: English
  • Copyright: © North Holland 1994
  • Published: February 18, 1994
  • Imprint: North Holland
  • eBook ISBN: 9780080872919

About the Serial Editor

Gregory Karpilovsky

Affiliations and Expertise

Department of Mathematics, California State University, Chico, CA,

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