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Mathematics - Algebra | Gröbner Bases and the Computation of Group Cohomology

Gröbner Bases and the Computation of Group Cohomology

Series: Lecture Notes in Mathematics, Vol. 1828

Green, David J.

2003, XII, 144 p.

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  • About this book

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.

Content Level » Research

Keywords » Cohomology - Gröbner basis - algebra - cohomology of finite groups - computational homological algebra - noncommutative Gröbner bases

Related subjects » Algebra

Table 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.

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