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The Isomorphism Theorems of Frobenius, Hopf and Gelfand—Mazur

1991; Springer Nature; Linguagem: Inglês

10.1007/978-1-4612-1005-4_11

2197-5612

Max Koecher, Reinhold Remmert,

Commutative Algebra and Its Applications

1. In the second half of the nineteenth century, many other hypercomplex systems were discovered and investigated, in addition to that of the quaternions. Especially in England, this became almost an art and was held in high esteem. Shortly after the discovery of quaternions and before the introduction of matrices, John T. GRAVES and Arthur CAYLEY devised the non-associative division algebra of octonions (also called octaves). Hamilton introduced, in his “Lectures on quaternions” of 1853, biquaternions, that is quaternions with complex coefficients, and noted that they do not form a division algebra. William Kingdon CLIFFORD (1845–1879) created in 1878, the associative algebras now called after him.