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حول تمثيل بعض انواع زمرلي وجبورلD == On Representation Of Some Types Of Lie Groups And Lie Algebras
Author name:
زينب صبحي مصطفى
Supervisor name:
سعد عويد بديوي
General topic:
Mathematics
Specific topic:
Mathematics
Degree:
Master
University:
Mustansiriyah University - College Of Science - Department Of Mathematics
Language:
English
University location:
Baghdad
First pages:
27T1143 - p.pdf
Abstract:
In this work, exploiting actions of special unitary, special linear matrix Lie groups SU(2), SL(2), a new adjiont representations ????????1, ????????2 are presented. Analogously, considering actions of the associated matrix Lie algebras ????????(2) and ????????(2) on themselves, a new adjoint representations ????????1 and ????????2 are obtained.We show that the adjoint representations ???????? : ????→????????(????), is completely determined by the generators of G and basis of ????. In particular, ????????1 : ????????(2)→????????(????????(2)),????????2 : ????????(2)→????????(????????(2)) depending only on the elements of the basis of ????????(2), ????????(2) and generators of SU(2), we prove that ????????1,????????2 are completely determined by generators of SU(2) and basis of ????????(2), ????????(2). Also, We show that the adjoint representations ???????? : ????→????????(????), is completely determined by the generators and basis of ????. In particular, ????????1 : ????????(2)→????????(????????(2)),????????2 : ????????(2)→????????(????????(2)) depending only on the elements of the basis and generators of ????????(2), ????????(2), we prove that ????????1,????????2 are completely determined by generators and basis of ????????(2), ????????(2).Moreover, the direct sums ????????1⨁????????2, ????????1⨁????????2, tensor products ????????1⊗????????2, ????????1⊗????????2 and duals ????????1̂, ????????2̂,????????1̂, ????????2̂ representations have been computed in details.
