Примери за използване на Lie algebras на Английски и техните преводи на Български
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Exceptional Lie algebras.
In the same letter he conjectured other theorems about Lie algebras.
Later Killing was to examine the Lie algebras associated with Lie groups.
In 1987 Zelmanov solved one of the big open questions in the theory of Lie algebras.
Kostrikin, in 1959,proved that such Lie algebras were indeed locally nilpotent.
The most remarkable part of this work is his discovery of the exceptional simple Lie algebras.
Elie Cartan worked on continuous groups, Lie algebras, differential equations and geometry.
Lie algebras were introduced by Lie in about 1870 in his work on differential equations.
In a long series of papers he applied Lie algebras to problems of theoretical physics.
Between 1968 and1972 Gelfand produced a series of important papers on the cohomology of infinite dimensional Lie algebras.
The exceptional simple Lie algebras are the subject of the final Section 18 of Killing's paper.
It was on algebras, now called Malcev algebras, which are natural generalisations of Lie algebras.
Killing introduced Lie algebras in Programmschrift(1884) published by the Lyceum Hosianum in Braunsberg.
In his Programmschrift he translated this geometrical aim into the problem of classifying all finite dimensional real Lie algebras.
Lectures by Weyl on Lie algebras in 1934-35 introduced Albert to the theory of non-associative algebras. .
He is remembered for the Campbell-Baker-Hausdorff theorem which gives a formula for multiplication of exponentials in Lie algebras.
He wrote two books which rapidly became classics on Lie algebras, Lie algebras(1962)and Exceptional Lie algebras(1971).
However, he is most frequently remembered for the Campbell-Baker- Hausdorff theorem which gives a formula for multiplication of exponentials in Lie algebras.
Lectures by Weyl on Lie algebras were particularly stimulating but perhaps even more important was his introduction to Jordan algebras. .
Matsushima presented some of his results to Ehresmann 's seminar in Strasbourg,extending Cartan 's classification of complex irreducible Lie algebras to the case of real Lie algebras.
This was a classical result for finite dimensional Lie algebras but Zelmanov proved that the result also held also for infinite dimensional Lie algebras. .
This was a classical result for finite dimensional Lie algebras but Zelmanov solved a big open problem when he proved that the result also held for infinite dimensional Lie algebras. .
At this stage Killing was not aware of Lie 's work and therefore his definition of a Lie algebra was made quite independently of Lie. .
In 1948 Eilenberg, in a joint paper with Chevalley, gave an algebraic approach to the cohomology of Lie groups,using the Lie algebra as a basic object.
Zelmanov next set about proving that a Lie algebra with an Engel condition was locally nilpotent.
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.
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.
Rather he was examining conditions on the Lie algebra which he studied for their geometrical significance and only later did he try to relate the conditions to semisimple algebras. .
He then embarked on research which enabled him to prove that Cartan subalgebras of a Lie algebra are conjugate, but due to being out of touch with current research, he was to publish this result while unaware that Chevalley had already published a proof.
This led to combining the transformations in a way that Lie called an infinitesimal group, but which is not a group with our definition,rather what is today called a Lie algebra.