The greatest mathematical paper of all time

@article{Coleman1989TheGM,
  title={The greatest mathematical paper of all time},
  author={Amos J. Coleman},
  journal={The Mathematical Intelligencer},
  year={1989},
  volume={11},
  pages={29-38}
}
  • A. J. Coleman
  • Published 1 June 1989
  • Mathematics
  • The Mathematical Intelligencer
ConclusionWhy do I think that Z.v.G.II was an epoch-making paper?(1)It was the paradigm for subsequent efforts to classify the possible structures for any mathematical object. Hawkins [15] documents the fact that Killing’s paper was the immediate inspiration for the work of Cartan, Molien, and Maschke on the structure of linearassociative algebras which culminated in Wedderburn’s theorems. Killing’s success was certainly an example which gave Richard Brauer the will to persist in the attempt to… 

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References

SHOWING 1-10 OF 32 REFERENCES

Weight spaces and irreducible representations of simple Lie algebras.

sentation of L admitting y j 3C as a weight function. In this paper we make a further study of the relationship between the representations of L and their weight spaces. 1. Weight spaces of

Theory of Groups of Finite Order

Preface to the second edition Preface to the first edition 1. On permutations 2. The definition of a group 3. On the simpler properties of a group which are independent of its mode of representation

Infinite-dimensional Lie algebras

1. Basic concepts.- 1. Preliminaries.- 2. Nilpotency and solubility.- 3. Subideals.- 4. Derivations.- 5. Classes and closure operations.- 6. Representations and modules.- 7. Chain conditions.- 8.

Standard Representations of Simple Lie Algebras

  • I. Bouwer
  • Mathematics
    Canadian Journal of Mathematics
  • 1968
Let L be any simple finite-dimensional Lie algebra (defined over the field K of complex numbers). Cartan's theory of weights is used to define sets of (algebraic) representations of L that can be

On infinite root systems

We define in an axiomatic fashion the concept of a set of root data that generalizes the usual concept of root system of a Kac-Moody Lie algebra. We study these objects from a purely formal and

SIMPLE IRREDUCIBLE GRADED LIE ALGEBRAS OF FINITE GROWTH

We classify the simple graded Lie algebras , for which the dimension of the space grows as some power of , under the additional assumption that the adjoint representation of on is irreducible. From

Treue Darstellung Liescher Ringe.

Ein Liescher Ring £ mit den Elementen , , ... ist hinsichtlich der distributiven Multiplikation durch die Regeln aa = 0, (ab) c + (bc) a + (ca) b = 0 gekennzeichnet. Es folgt ab + ba = (a + b) (a +

Theorie der Transformationsgruppen I

Einleitung Erster Abschnitt: Allgemeine Eigenschaften der endlichen continuirlichen Transformationsgruppen Zweiter Abschnitt: Theorie der Beruhrungstransformationen und der Gruppen von