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The discrete octonionic Stokes' formula revisited

Rolf Sören Kraußhar, Anastasiia Legatiukand, Dmitrii Legatiuk

Abstract

In a previous work [arXiv:2211.02945] we made an attempt to set up a discrete octonionic Stokes' formula. Due to an algebraic property that we have not considered in that attempt, the formula however turned out to involve an associator term in addition to a change of sign that we already observed earlier. This associator term has an impact on the final result. In this paper we carefully revise this discrete Stokes formula taking into account this additional term. In fact the result that we now obtain is much more in line with the results that one has in the continuous setting.

The discrete octonionic Stokes' formula revisited

Abstract

In a previous work [arXiv:2211.02945] we made an attempt to set up a discrete octonionic Stokes' formula. Due to an algebraic property that we have not considered in that attempt, the formula however turned out to involve an associator term in addition to a change of sign that we already observed earlier. This associator term has an impact on the final result. In this paper we carefully revise this discrete Stokes formula taking into account this additional term. In fact the result that we now obtain is much more in line with the results that one has in the continuous setting.
Paper Structure (3 sections, 1 theorem, 17 equations)

This paper contains 3 sections, 1 theorem, 17 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Discrete octonionic Stokes' formula revisited

Key Result

theorem 1

The discrete Stokes' formula for the whole lattice $h\mathbb{Z}^{8}$ is given by for all discrete functions $f$ and $g$ such that the series converge, where the index sets $I_{s}$, $s=1,\ldots,7$ are given by

Theorems & Definitions (2)

  • theorem 1
  • proof