The space-time sedenions algebra encloses eight groups of values, which are differed with respect to spatial and time inversion.

 

Here indexes t and r indicate the transformations (r for spatial inversion and t for time inversion), which change the corresponding values. All introduced values can be integrated into one space-time object named space-time sedenion, which is defined by the following expression:

 

The multiplication and commutation rules for the basis elements are similar to quaternionic rules. They are presented in tables 1 and 2. 

 

 

 

 

The publications conserning of space-time sedenions

 

1. V.L. Mironov, S.V. Mironov — Associative space-time sedenions,  http://vixra.org/abs/1401.0162 (2014).
2. V.L. Mironov, S.V. Mironov - Reformulation of relativistic quantum mechanics and field theory equations with space - time sedenions, http://vixra.org/abs/1402.0157

 

V.L.Mironov, S.V.Mironov – Associative space-time sedenions and their application in relativistic quantum mechanics and fieldtheory // Applied mathematics, 6(1), 46-56 (2015).

 

We present an alternative sixteen-component hypercomplex scalar-vector values named "space-time sedenions", generating associative noncommutative space-time Clifford algebra. The generalization of relativistic quantum mechanics and field theory equations based on sedenionic wave function and space-time operators is discussed.