Hypercomplex numbers, lie groups, and the creation of group representation theory

@article{Hawkins1972HypercomplexNL,
  title={Hypercomplex numbers, lie groups, and the creation of group representation theory},
  author={Thomas Hawkins},
  journal={Archive for History of Exact Sciences},
  year={1972},
  volume={8},
  pages={243-287}
}
  • Thomas Hawkins
  • Published 1972
  • Mathematics
  • Archive for History of Exact Sciences
The greatest mathematical paper of all time
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
Generalized group determinant gives a necessary and sufficient condition for a subset of a finite group to be a subgroup
Abstract We generalize the concept of the group determinant and prove a necessary and sufficient novel condition for a subset to be a subgroup. This development is based on the group determinant work
Die physikalischen Arbeiten des jungen B. L. van der Waerden
Die vorliegende Arbeit behandelt den Prozess der Mathematisierung der Quantenmechanik aus mathematikhistorischer Perspektive am Beispiel der Einfuhrung der gruppentheoretischen Methode zwischen 1926
Assessing Non-Atomicity in Groups of Divisibility
An integral domain D is atomic if every non-zero non-unit is a product of irreducibles. More generally, D is quasi-atomic if every non-zero non-unit divides some product of atoms. Arbitrary integral
Nikolay Luzin, his students, adversaries, and defenders (notes on the history of Moscow mathematics, 1914-1936)
This is historical-mathematical and historical notes on Moscow mathematics 1914-1936. Nikolay Luzin was a central figure of that time. Pavel Alexandroff, Nina Bari, Alexandr Khinchin, Andrey
A history of Galois fields
This paper stresses a specific line of development of the notion of finite field, from Evariste Galois's 1830 ''Note sur la theorie des nombres,'' and Camille Jordan's 1870 Traite des substitutions
Coset Group Construction of Multidimensional Number Systems
TLDR
It is shown that extensions of real numbers in two or more dimensions follow naturally from the closure property of finite coset groups adding insight into the utility of multidimensional number systems in describing symmetries in nature.
Alternative Routes to Representation Theory
The correspondence between Dedekind and Frobenius makes it clear that if Dedekind had not decided to introduce and study group determinants—a subject with no established tradition and really outside
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 61 REFERENCES
The origins of the theory of group characters
1. Introductory Remarks The following is intended as a first step towards the writing of the history of the representation heory of finite groups. The central figure is, of course, Georg Frob niu
über die Erzeugung der Invarianten durch Integration
Es liege eine endliche Gruppe von diskreten Substitutionen vor, die sieh auf die Variablen x 1, x 2,...x n beziehen. Dann gibt es ein einfaches Verfahren, um alle Invarianten dieser Gruppe
Representation theory of finite groups and associated algebras
A loom sley capable of use in high speed looms comprises a substantially tubular member, said tubular member having attached thereto a race board plate and a reed support device, said race board
Élie Cartan and his mathematical work
After a long illness Élie Cartan died on May 6, 1951, in Paris. His death came at a time when his reputation and the influence of his ideas were in full ascent. Undoubtedly one of the greatest
The classical groups : their invariants and representations
In this renowned volume, Hermann Weyl discusses the symmetric, full linear, orthogonal, and symplectic groups and determines their different invariants and representations. Using basic concepts from
Eliakim Hastings Moore
...
1
2
3
4
5
...