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Examples of G-Hom-Associative Algebras
Mälardalens universitet, Akademin för utbildning, kultur och kommunikation.
2024 (engelsk)Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgave
Abstract [en]

In this thesis we look at hom-associative algebras (which turn out to be exactly the G1-hom-associative algebras), by, in two and three dimensions, trying to find the structure constants for which an algebra becomes hom-associative when the homomorphism 𝛼 is defined as different matrix units. These algebras are also hom-Lie admissible (or G6-hom-associative, which turn out to be the same thing) with a commutator, so we also find the commutator for each of these hom-Lie admissible algebras. We end up finding every hom-associative and hom-Lie algebra for 𝛼 defined as each 2×2 matrix unit in two dimensions, each 3×3 matrix unit in three dimensions when the problem is mapped to one dimension, for three 3×3 matrix units in three dimensions when the problem is mapped to two dimensions (but with the commutators not having been calculated), and only a few hom-associative algebras and hom-Lie algebras for one 3×3 matrix unit in the full three dimensions. We also compare the results for the different values of 𝛼, and find that in 𝑛 dimensions it is possible to find the values of the structure constants for all 𝑛2 different 𝛼:s simply by finding all of the solutions for 𝑛 different 𝛼:s (chosen in a specific way) and then permutating all of the indices.

sted, utgiver, år, opplag, sider
2024. , s. 226
Emneord [en]
G-hom-associative algebra, hom-associative algebra, hom-Lie admissible algebra
HSV kategori
Identifikatorer
URN: urn:nbn:se:mdh:diva-65923OAI: oai:DiVA.org:mdh-65923DiVA, id: diva2:1835595
Fag / kurs
Mathematics/Applied Mathematics
Veileder
Examiner
Tilgjengelig fra: 2024-02-09 Laget: 2024-02-06 Sist oppdatert: 2024-02-09bibliografisk kontrollert

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Examples of G-Hom-Associative Algebras(1014 kB)76 nedlastinger
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