
TL;DR
This paper introduces a new class of commutative Euclidean group algebras $\
Contribution
It constructs and analyzes a new family of Euclidean algebras $\
Findings
The algebra $\
The zero divisor set has Lebesgue measure zero.
Analytic function theory analogous to complex analysis is developed.
Abstract
We introduce a new example of unital commutative -dimensional group algebra for . The algebra and the complex numbers are astonishingly alike. The zero divisor set of the algebra has Lebesgue -measure zero. The formula for the Haar measure is established. Also, the analytic function theory in for that similar to the classical theory in is introduced. This includes the Cauchy-Riemann equations, mean-value theorem and Louisville theorem.
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Taxonomy
TopicsMathematical and Theoretical Analysis · Matrix Theory and Algorithms · Algebraic and Geometric Analysis
