Clifford algebras of $p$-central sets
Adam Chapman

TL;DR
The paper introduces a generalized Clifford algebra related to p-central sets, explores its structure using central simple algebra theory, and applies graph theory to solve specific cubic equations in algebraic integers.
Contribution
It generalizes the concept of Clifford algebras for p-central sets and develops a graph-theoretic method for analyzing their generators when p=3.
Findings
Established a structure theory for the generalized Clifford algebra
Proposed a graph-theoretic approach for p=3 case
Derived solutions to a specific cubic equation in algebraic integers
Abstract
A generalization of the term "generalized Clifford algebras" (as appears in papers on advances in applied Clifford algebras) is introduced. This algebra is studied by means of structure theory of central simple algebras. A graph theoretical approach is proposed for studying the generating set of this algebra in case where the prime number under discussion is three. Finally, it is shown how to obtain solutions in to the equation in where is the primitive third root of unity.
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Taxonomy
TopicsAlgebraic and Geometric Analysis · Mathematical Analysis and Transform Methods · Geometric and Algebraic Topology
