A non-associative structure in the group algebra of PSL2(Z)
The group PSL2(Z) is the quotient group of SL2(Z) modulo the normal subgroup {-I,I}. The group algebra A of PSLâ‚‚(Z) is the associative algebra for which the elements of PSL2(Z) form a basis. We will study the non-associative structure which is the Lie algebra structure in A with the operation of L...
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oai:animorepository.dlsu.edu.ph:etd_bachelors-190812022-02-11T06:17:52Z A non-associative structure in the group algebra of PSL2(Z) Tan, Christian Benedict Zaraspe, Ivan Stephen The group PSL2(Z) is the quotient group of SL2(Z) modulo the normal subgroup {-I,I}. The group algebra A of PSLâ‚‚(Z) is the associative algebra for which the elements of PSL2(Z) form a basis. We will study the non-associative structure which is the Lie algebra structure in A with the operation of Lie bracket taken as the commutator. Using several computations involving nested commutators, we express the results of our computations in terms of the standard basis for A and we discover that there are invariant subspaces under some adjoint maps. We also show some interesting properties of the said subspaces. 2019-01-01T08:00:00Z text https://animorepository.dlsu.edu.ph/etd_bachelors/18568 Bachelor's Theses English Animo Repository Mathematics |
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Mathematics |
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Mathematics Tan, Christian Benedict Zaraspe, Ivan Stephen A non-associative structure in the group algebra of PSL2(Z) |
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The group PSL2(Z) is the quotient group of SL2(Z) modulo the normal subgroup {-I,I}. The group algebra A of PSLâ‚‚(Z) is the associative algebra for which the elements of PSL2(Z) form a basis. We will study the non-associative structure which is the Lie algebra structure in A with the operation of Lie bracket taken as the commutator. Using several computations involving nested commutators, we express the results of our computations in terms of the standard basis for A and we discover that there are invariant subspaces under some adjoint maps. We also show some interesting properties of the said subspaces. |
| format |
text |
| author |
Tan, Christian Benedict Zaraspe, Ivan Stephen |
| author_facet |
Tan, Christian Benedict Zaraspe, Ivan Stephen |
| author_sort |
Tan, Christian Benedict |
| title |
A non-associative structure in the group algebra of PSL2(Z) |
| title_short |
A non-associative structure in the group algebra of PSL2(Z) |
| title_full |
A non-associative structure in the group algebra of PSL2(Z) |
| title_fullStr |
A non-associative structure in the group algebra of PSL2(Z) |
| title_full_unstemmed |
A non-associative structure in the group algebra of PSL2(Z) |
| title_sort |
non-associative structure in the group algebra of psl2(z) |
| publisher |
Animo Repository |
| publishDate |
2019 |
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https://animorepository.dlsu.edu.ph/etd_bachelors/18568 |
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1772835346950651904 |