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Universal Algebra Applied to Hom-Associative Algebras, and More
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. (Mathematics and Applied Mathematics)ORCID iD: 0000-0001-6140-180X
University of Haute Alsace, LMIA.
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. (Mathematics and Applied Mathematics)ORCID iD: 0000-0003-4554-6528
2014 (English)In: Algebra, Geometry, and Mathematical Physics: AGMP, Mulhouse, France, October 2011, Springer Berlin/Heidelberg, 2014, 157-199 p.Conference paper (Refereed)
Abstract [en]

The purpose of this paper is to discuss the universal algebra theory of hom-algebras. This kind of algebra involves a linear map which twists the usual identities. We focus on hom-associative algebras and hom-Lie algebras for which we review the main results. We discuss the envelopment problem, operads, and the Diamond Lemma; the usual tools have to be adapted to this new situation. Moreover we study Hilbert series for the hom-associative operad and free algebra, and describe them up to total degree equal 8 and 9 respectively.

Place, publisher, year, edition, pages
Springer Berlin/Heidelberg, 2014. 157-199 p.
Series
Springer Proceedings in Mathematics & Statistics, ISSN 2194-1009 ; 85
Keyword [en]
hom-Lie algebras, hom-associative algebra, operad, universal algebra, enveloping hom-algebra, diamond lemma, Hilbert series
National Category
Mathematics Algebra and Logic
Research subject
Mathematics/Applied Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-24088DOI: 10.1007/978-3-642-55361-5_11ISI: 000347610400011Scopus ID: 2-s2.0-84939444285ISBN: 978-3-642-55360-8 (print)OAI: oai:DiVA.org:mdh-24088DiVA: diva2:682972
Conference
Algebra, Geometry and Mathematical Physics Conference, University of Haute Alsace, France, October 2011.
Available from: 2013-12-31 Created: 2013-12-31 Last updated: 2016-01-18Bibliographically approved

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CiteExportLink to record
Permanent link

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Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
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  • asciidoc
  • rtf