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TitleComputing homology using generalized Gröbner bases
Author(s) Becky Eide Hall
TypeArticle in Journal
AbstractA well-known theorem due to Manin gives a relationship between modular symbols for a congruence subgroup Γ_0(N) of SL_2(Z) and the homology of the modular curve X_0(N) , making the homology easier to compute. A corresponding theorem of Ash (1992) allows for explicit computation of the homology of congruence subgroups of SL_3(Z) with coefficients in a given representation V. Applying Ashʼs theorem requires finding the invariants of an ideal in the group algebra Z[SL_3(Z)] on V. We employ a generalized notion of Gröbner bases for a non-commutative group algebra in order to determine a minimal generating set for the desired ideal.
KeywordsNon-commutative group algebra, Gröbner bases, Congruence subgroups, SL 3 ( Z )
ISSN0747-7171
URL http://www.sciencedirect.com/science/article/pii/S0747717113000138
LanguageEnglish
JournalJournal of Symbolic Computation
Volume54
Number0
Pages59 - 71
Year2013
Edition0
Translation No
Refereed No
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