Representations of Elementary Abelian p-Groups and Vector Bundles

Inbunden, Engelska, 2016

Del 208 i serien Cambridge Tracts in Mathematics

1 521 kr

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Beskrivning

Questions about modular representation theory of finite groups can often be reduced to elementary abelian subgroups. This is the first book to offer a detailed study of the representation theory of elementary abelian groups, bringing together information from many papers and journals, as well as unpublished research. Special attention is given to recent work on modules of constant Jordan type, and the methods involve producing and examining vector bundles on projective space and their Chern classes. Extensive background material is provided, which will help the reader to understand vector bundles and their Chern classes from an algebraic point of view, and to apply this to modular representation theory of elementary abelian groups. The final section, addressing problems and directions for future research, will also help to stimulate further developments in the subject. With no similar books on the market, this will be an invaluable resource for graduate students and researchers working in representation theory.

Produktinformation

Utgivningsdatum:2016-11-17
Mått:152 x 229 x 24 mm
Vikt:680 g
Format:Inbunden
Språk:Engelska
Serie:Cambridge Tracts in Mathematics
Antal sidor:348
Förlag:Cambridge University Press
ISBN:9781107174177

Utforska kategorier

Algebra inom Naturvetenskap och teknik
Grupper och gruppteori inom Naturvetenskap och teknik
Matematik inom Naturvetenskap och teknik

Mer om författaren

David J. Benson is currently the Sixth Century Professor of Mathematics at the University of Aberdeen. He has authored a number of books, including Representations and Cohomology (Cambridge, 1991) and Polynomial Invariants of Finite Groups (Cambridge, 1993).

Recensioner i media

'In summary, this book provides a thorough introduction to the theory of the correspondence between modular representations of elementary abelian groups and vector bundles over projective space. In it the reader will find results from the literature, as well as new contributions to the field. It provides all of the background necessary to understand the material, and provides a lot of interesting examples as well as open problems.' Alan Koch, Mathematical Reviews

Innehållsförteckning

Preface; Introduction; 1. Modular representations and elementary abelian groups; 2. Cyclic groups of order p; 3. Background from algebraic geometry; 4. Jordan type; 5. Modules of constant Jordan type; 6. Vector bundles on projective space; 7. Chern classes; 8. Modules of constant Jordan type and vector bundles; 9. Examples; 10. Restrictions coming from Chern numbers; 11. Orlov's correspondence; 12. Phenomenology of modules over elementary abelian p-groups; A. Modules for Z/p; B. Problems; References; Index.