transfinite arithmetic, cardinal arithmetic, ordinal arithmetic
prime field, p-adic integer, p-adic rational number, p-adic complex number
arithmetic geometry, function field analogy
symmetric monoidal (∞,1)-category of spectra
The tessarines are an algebra over the real numbers. Every tessarine $t$ may be represented as
where the basis elements satisfy the following products:
$\times$ | i | j | k |
---|---|---|---|
i | -1 | k | -j |
j | k | +1 | i |
k | -j | i | -1 |
and conjugation $t^* = a_0 - a_1 i - a_2 j - a_3k$.
These are closely related to the quaternions, as the generators satisfy similarly-looking relations.
The tessarines are also referred to as bicomplex numbers since they may be obtained using the generalization of the Cayley-Dickson construction applied on the complex numbers.
Elena Luna-Elizarrarás, Michael Shapiro, Daniele Struppa (2013) Bicomplex Holomorphic Functions: the algebra, geometry and analysis of bicomplex numbers. Birkhauser ISBN 978-3-319-24868-4
Fidelis Zanetti de Castro, Marcos Eduardo Valle. A Broad Class of Discrete-Time Hypercomplex-Valued Hopfield Neural Networks. Neural Networks 122, February 2020, Pages 54-67. (doi)
Last revised on November 3, 2023 at 05:26:17. See the history of this page for a list of all contributions to it.