Gröbner Bases and the Computation of Group Cohomology

2003
ISBN: 978-3-540-20339-1
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 1828, 144 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 248 g

Reihe: Lecture Notes in Mathematics

This monograph develops the Gröbner basis methods needed to perform efficient state-of- the-art calculations in the cohomology of finite groups. Results obtained include the first counterexample to the conjecture that the ideal of essential classes squares to zero. The context is J.F. Carlson's minimal resolutions approach to cohomology computations.

Zielgruppe

Research

Autoren/Hrsg.

Green, David J.

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Homologische Algebra
• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie

Inhaltsverzeichnis

Introduction.- Part I Constructing minimal resolutions: Bases for finite-dimensional algebras and modules; The Buchberger Algorithm for modules; Constructing minimal resolutions.- Part II Cohomology ring structure: Gröbner bases for graded commutative algebras; The visible ring structure; The completeness of the presentation.- Part III Experimental results: Experimental results.- A. Sample cohomology calculations.- Epilogue.- References.- Index.