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Twisted derivations, quasi-hom-Lie algebras and their quasi-deformations
Mälardalen University, School of Education, Culture and Communication.
2017 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
Abstract [en]

Quasi-hom-Lie algebras (qhl-algebras) were introduced by Larsson and Silvestrov (2004) as a generalisation of hom-Lie algebras, which are a deformation of Lie algebras. Lie algebras are defined by an operation called bracket, [·,·], and a three-term Jacobi identity. By the theorem from Hartwig, Larsson, and Silvestrov (2003), this bracket and the three-term Jacobi identity are deformed into a new bracket operation, <·,·>, and a six-term Jacobi identity, making it a quasi-hom-Lie algebra.

Throughout this thesis we deform the Lie algebra sl2(F), where F is a field of characteristic 0. We examine the quasi-deformed relations and six-term Jacobi identities of the following polynomial algebras: F[t], F[t]/(t2), F[t]/(t3), F[t]/(t4), F[t]/(t5), F[t]/(tn), where n is a positive integer ≥2, and F[t]/((t-t0)3). Larsson and Silvestrov (2005) and Larsson, Sigurdsson, and Silvestrov (2008) have already examined some of these cases, which we repeat for the reader's convenience.

We further investigate the following σ-twisted derivations, and how they act in the different cases of mentioned polynomial algebras: the ordinary differential operator, the shifted difference operator, the Jackson q-derivation operator, the continuous q-difference operator, the Eulerian operator, the divided difference operator, and the nilpotent imaginary derivative operator. We also introduce a new, general, σ-twisted derivation operator, which is σ(t) as a polynomial of degree k.

Place, publisher, year, edition, pages
2017. , 64 p.
Keyword [en]
quasi-hom-Lie algebra, hom-Lie algebra, Lie algebra, Twisted derivation, sigma derivation, quasi-Lie algebra, derivation, quasi deformation, quasi-deformation, twisted vector field, polynomial algebra, quotient ring
National Category
Algebra and Logic
Identifiers
URN: urn:nbn:se:mdh:diva-35553OAI: oai:DiVA.org:mdh-35553DiVA: diva2:1105479
Subject / course
Mathematics/Applied Mathematics
Presentation
2017-06-01, U3-083, Högskoleplan 1, Västerås, 11:49 (English)
Supervisors
Examiners
Available from: 2017-07-03 Created: 2017-06-04 Last updated: 2017-07-03Bibliographically approved

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Algebra and Logic

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CiteExportLink to record
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Citation style
  • apa
  • harvard1
  • 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
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Output format
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