By W. A. de Graaf

the purpose of the current paintings is two-fold. to start with it goals at a giving an account of many current algorithms for calculating with finite-dimensional Lie algebras. Secondly, the booklet presents an advent into the speculation of finite-dimensional Lie algebras. those topic parts are in detail similar. to start with, the algorithmic point of view usually invitations a distinct method of the theoretical fabric than the only taken in a variety of different monographs (e.g., [42], [48], [77], [86]). certainly, on a variety of events the information of sure algorithms permits us to acquire a simple facts of theoretical effects (we point out the facts of the Poincaré-Birkhoff-Witt theorem and the facts of Iwasawa's theorem as examples). additionally proofs that comprise algorithmic structures are explicitly formulated as algorithms (an instance is the isomorphism theorem for semisimple Lie algebras that constructs an isomorphism in case it exists). Secondly, the algorithms can be utilized to reach at a greater figuring out of the idea. acting the algorithms in concrete examples, calculating with the strategies concerned, rather brings the speculation of life.

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