Del 0 - Algebra and Applications

Cohomology Rings of Finite Groups

With an Appendix: Calculations of Cohomology Rings of Groups of Order Dividing 64

Häftad, Engelska, 2010

AvJon F. Carlson,L. Townsley,Luís Valero-Elizondo,Mucheng Zhang

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This text offers comprehensive coverage of group cohomology, from introductory material through the most recent developments in the field. The primary motivation for this book is the interaction of group cohomology with representation theory, especially the geometry of support varieties over cohomology rings. The appendices, comprising computer calculations of the mod-2 cohomology rings of the groups whose orders divide 64, provide information useful for further developments in the field. A unique feature of this text is that it includes the concepts that are the subject of the calculations and are the source of some of the motivating conjectures for the computations. The programs for computing the cohomology rings were executed in the MAGMA computer algebra language. The text is a valuable resource for researchers in group cohomology and related disciplines. In addition, the book could be used as the text for an advanced graduate class or a graduate seminar.

Produktinformation

Utgivningsdatum2010-12-09
Mått155 x 235 x 43 mm
Vikt1 183 g
FormatHäftad
SpråkEngelska
SerieAlgebra and Applications
Antal sidor776
FörlagSpringer
ISBN9789048163854

Tillhör följande kategorier

1. Homological Algebra.- 2. Group Algebras.- 3. Projective Resolutions.- 4. Cohomology Products.- 5. Spectral Sequences.- 6. Norms and the Cohomology of Wreath Products.- 7. Steenrod Operations.- 8. Varieties and Elementary Abelian Subgroups.- 9. Cohomology Rings of Modules.- 10. Complexity and Multiple Complexes.- 11. Duality Complexes.- 12. Transfers, Depth and Detection.- 13. Subgroup Complexes.- 14. Computer Calculations and Completion Tests.- Appendices: Calculations of the Cohomology Rings of Groups of Order Dividing 64.- A— Notation and References.- B— Groups of Order 8.- C— Groups of Order 16.- D— Groups of Order 32.- E— Groups of Order 64.- F— Tables of Krull Dimension and Depth.- G— Tables of Hilbert / Poincaré Series.- References.

From the reviews: "The cohomology of groups was developed to be ... a powerful tool in the study of group representations. ... Some other books concerning the cohomology of finite groups have appeared, but they are at least ten years old, and the computational tools that have been developed since then, make this book to be really valuable for both professionals and students. ... This book is almost self-contained and it is very useful ... for all of those that are using the cohomology instruments in their work." (Viorel Mihai Gontineac, Zentralblatt MATH, Vol. 1056 (7), 2005)