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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| Main Authors: | , |
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| Format: | text |
| Language: | English |
| Published: |
Animo Repository
2019
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| Subjects: | |
| Online Access: | https://animorepository.dlsu.edu.ph/etd_bachelors/18568 |
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| Institution: | De La Salle University |
| Language: | English |
| Summary: | 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. |
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