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 š¯›¼ 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 š¯›¼ defined as each 2Ć—2 matrix unit in two dimensions, each 3Ć—3 matrix unit in three dimensions when the problem is mapped to one dimension, for three 3Ć—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 3Ć—3 matrix unit in the full three dimensions. We also compare the results for the different values of š¯›¼, and find that in š¯‘› dimensions it is possible to find the values of the structure constants for all š¯‘›2 different š¯›¼:s simply by finding all of the solutions for š¯‘› different š¯›¼:s (chosen in a specific way) and then permutating all of the indices.
| Identifer | oai:union.ndltd.org:UPSALLA1/oai:DiVA.org:mdh-65923 |
| Date | January 2024 |
| Creators | Modin, Felicia |
| Publisher | MƤlardalens universitet, Akademin fƶr utbildning, kultur och kommunikation |
| Source Sets | DiVA Archive at Upsalla University |
| Language | English |
| Detected Language | English |
| Type | Student thesis, info:eu-repo/semantics/bachelorThesis, text |
| Format | application/pdf |
| Rights | info:eu-repo/semantics/openAccess |
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