Gröbner Bases and the Computation of Group Cohomology [electronic resource].
Material type: TextSeries: Lecture Notes in Mathematics ; 1828Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2003Description: XII, 144 p. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783540396802Subject(s): Mathematics | Algebra | Group theory | Mathematics | Group Theory and Generalizations | Associative Rings and AlgebrasAdditional physical formats: Printed edition:: No titleDDC classification: 512.2 LOC classification: QA174-183Online resources: Click here to access onlineCurrent library | Home library | Call number | Materials specified | URL | Status | Date due | Barcode |
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IMSc Library | IMSc Library | Link to resource | Available | EBK1152 |
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.
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.
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