Примери за използване на Semisimple на Английски и техните преводи на Български
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He then turned to representations of semisimple Lie groups.
The classification of the semisimple Lie algebras by Killing was one of the finest achievements in the whole of mathematical research.
During this time he worked on representations of semisimple Lie groups.
In later work on group algebras both for semisimple Lie groups and more general groups, he showed that every derivation is inner.
He then turned his attention to representations of semisimple Lie groups.
The main tools in the classification of the semisimple Lie algebras are Cartan subalgebras and the Cartan matrix both first introduced by Killing.
He made a detailed analysis of the infinite-dimensional representations of the semisimple Lie groups.
He studied the structure of semisimple alternative rings in 1932, proving that such a ring is a direct sum of simple alternative algebras which he classified.
At this time he discovered the'Dynkin diagram' approach to the classification of the semisimple Lie algebras.
In particular his theory of representations of semisimple groups, developed during 1924-26, was very deep and considered by Weyl himself to be his greatest achievement.
This work formed the basis for later work by Harish-Chandra on representations of semisimple Lie groups.
Zassenhaus had conjectured that every semisimple Lie algebra L over a field of prime characteristic, with[L, L]= L, is the direct sum of simple ideal and Matsushima was able to construct a counterexample.
In 1907 Wedderburn published what is perhaps his most famous paper on the classification of semisimple algebras.
We should make it clear that although he was examining conditions on a Lie algebra which essentially made it semisimple(that is having no soluble ideals) in Programmschrift, he was not aiming at such a classification at this stage.
This work came out of Dynkin trying to understand the papers by Weyl andby van der Waerden on semisimple Lie groups.
In this paper On hypercomplex numbers which appeared in the Proceedings of the London Mathematical Society,he showed that every semisimple algebra is a direct sum of simple algebras and that a simple algebra was a matrix algebra over a division ring.
In his 1949 paper Iwasawa gives what is now known as the'Iwasawa decomposition' of a real semisimple Lie group.
When Killing wrote to Engel on 27 April 1887 he had come up with the definition of a semisimple Lie algebra(his definition that such an algebra had no abelian ideals is equivalent to the definition that such an algebra has no soluble ideals).
In addition to the topics we mentioned above,we should single out his work on the characters of the semisimple Lie groups between 1954 and 1956.
In many ways Cartan was so successful in presenting Killing's classification of the semisimple Lie algebras in rigorous and complete single work, that Killing has not received as much acclaim for his remarkable achievements as one might have expected.
He did this quite independently of Lie(and not it would appear in a manner which Lie found satisfactory), andit was Cartan who completed the classification of semisimple Lie algebras in 1900.
He won the Cole prize from the American Mathematical Society in 1954 for his papers on representations of semisimple Lie algebras and groups, and particularly for his paper On some applications of the universal enveloping algebra of a semisimple Lie algebra which he had published in the Transactions of the American Mathematical Society in 1951.
He was working on the algebraic characterisation of the topology of the real semisimple Lie groups in 1940 when Germany invaded The Netherlands.
It was Harish-Chandra who extended the concept of a character of finite-dimensional representations of semisimple Lie groups to the case of infinite-dimensional representations;