# 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} }

## 46 Citations

The greatest mathematical paper of all time

- Mathematics
- 1989

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…

A Sturm‐Liouville equation on the crossroads of continuous and discrete hypercomplex analysis

- MathematicsMathematical Methods in the Applied Sciences
- 2021

Generalized group determinant gives a necessary and sufficient condition for a subset of a finite group to be a subgroup

- Mathematics
- 2019

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

- Philosophy
- 2018

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

- Mathematics
- 2017

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)

- Mathematics
- 2017

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

- Mathematics
- 2016

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

- MathematicsSymmetry
- 2014

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

- Mathematics
- 2013

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…

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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…

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