Lie Algebra and Representation Theory

Assignment Requirements

Try to use the below  structure :
Background:
– Introduce Lie algebras, ideals, representations of Lie algebras and irreducibility (half page)
– Discuss the classification of simple Lie algebras, and briefly discuss what is known about Casimir operators (or invariants, etc) in this context. In particular, mention the connection with Schur’s Lemma and the eigenvalue of the Casimir invariant on an irreducible representation as a means of explain the importance of Casimir invariants. (One and half pages)
use references of :
* Quesne ( title : Casimir operators of semidiret sum lie algebras)
another like :
Campoamor ,Perroud,Aizawa, (Perelomov and
Popov 1966, Popov and Perelomov 1967, Popov 1976,Nwachuku and Rashid 1976,
1977, Nwachuku 1979, and references therein).
– State the Proposition in Bourbaki related to Casimir invariant and ideal, and describe some special cases. (Half page)
– Discuss classification of all low dimensional Lie algebras (e.g. book by Winternitz & Snobl 2014), which includes non-semisimple ones, and related Casimir operators. (One page)

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