Nilpotent Quotients of Associative [Formula: see text]-Algebras and Augmentation Quotients of Baumslag-Solitar Groups

We describe the functionality of the package zalgs for the computer algebra system GAP. The package contains an implementation of the nilpotent quotient algorithm for finitely presented associative [Formula: see text]-algebras described in [3]. As an application of this algorithm we calculate augmen...

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Autor principal: Moede, Tobias
Formato: Online Artículo Texto
Lenguaje:English
Publicado: 2020
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7340925/
http://dx.doi.org/10.1007/978-3-030-52200-1_12
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author Moede, Tobias
author_facet Moede, Tobias
author_sort Moede, Tobias
collection PubMed
description We describe the functionality of the package zalgs for the computer algebra system GAP. The package contains an implementation of the nilpotent quotient algorithm for finitely presented associative [Formula: see text]-algebras described in [3]. As an application of this algorithm we calculate augmentation quotients, i.e. successive quotients of powers of the augmentation ideal I(G) of the integral group ring [Formula: see text], where G is a finitely presented group. We apply these methods to obtain conjectures for augmentation quotients of the Baumslag-Solitar groups BS(m, n) with [Formula: see text] equal to 0, 1 or a prime p.
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spelling pubmed-73409252020-07-08 Nilpotent Quotients of Associative [Formula: see text]-Algebras and Augmentation Quotients of Baumslag-Solitar Groups Moede, Tobias Mathematical Software – ICMS 2020 Article We describe the functionality of the package zalgs for the computer algebra system GAP. The package contains an implementation of the nilpotent quotient algorithm for finitely presented associative [Formula: see text]-algebras described in [3]. As an application of this algorithm we calculate augmentation quotients, i.e. successive quotients of powers of the augmentation ideal I(G) of the integral group ring [Formula: see text], where G is a finitely presented group. We apply these methods to obtain conjectures for augmentation quotients of the Baumslag-Solitar groups BS(m, n) with [Formula: see text] equal to 0, 1 or a prime p. 2020-06-06 /pmc/articles/PMC7340925/ http://dx.doi.org/10.1007/978-3-030-52200-1_12 Text en © Springer Nature Switzerland AG 2020 This article is made available via the PMC Open Access Subset for unrestricted research re-use and secondary analysis in any form or by any means with acknowledgement of the original source. These permissions are granted for the duration of the World Health Organization (WHO) declaration of COVID-19 as a global pandemic.
spellingShingle Article
Moede, Tobias
Nilpotent Quotients of Associative [Formula: see text]-Algebras and Augmentation Quotients of Baumslag-Solitar Groups
title Nilpotent Quotients of Associative [Formula: see text]-Algebras and Augmentation Quotients of Baumslag-Solitar Groups
title_full Nilpotent Quotients of Associative [Formula: see text]-Algebras and Augmentation Quotients of Baumslag-Solitar Groups
title_fullStr Nilpotent Quotients of Associative [Formula: see text]-Algebras and Augmentation Quotients of Baumslag-Solitar Groups
title_full_unstemmed Nilpotent Quotients of Associative [Formula: see text]-Algebras and Augmentation Quotients of Baumslag-Solitar Groups
title_short Nilpotent Quotients of Associative [Formula: see text]-Algebras and Augmentation Quotients of Baumslag-Solitar Groups
title_sort nilpotent quotients of associative [formula: see text]-algebras and augmentation quotients of baumslag-solitar groups
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7340925/
http://dx.doi.org/10.1007/978-3-030-52200-1_12
work_keys_str_mv AT moedetobias nilpotentquotientsofassociativeformulaseetextalgebrasandaugmentationquotientsofbaumslagsolitargroups

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