Gröbner Bases and the Computation of Group Cohomology

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.

List of contents

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.

Summary

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.

Product details

• Authors: David J. Green
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 15.01.2004
• EAN: 9783540203391
• ISBN: 978-3-540-20339-1
• No. of pages: 144
• Dimensions: 157 mm x 238 mm x 11 mm
• Weight: 242 g
• Illustrations: XII, 144 p.
• Series: Lecture Notes in Mathematics; Lecture Notes in Mathematics
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Arithmetic, algebra; Algebra, B, Group Theory, Mathematics and Statistics, Rings (Algebra), Group Theory and Generalizations, Associative rings, Associative Rings and Algebras