Classification of some graded not necessarily associative division algebras I
L. A. Wills-Toro

TL;DR
This paper classifies certain finite-group graded real division algebras, including classical and novel non-associative types, expanding understanding of their algebraic structures.
Contribution
It provides a classification of graded real division algebras with specific basis and scalar conditions, identifying both known and new non-associative division algebras.
Findings
Classified classical algebras: complex, quaternion, octonion
Discovered new non-associative division algebras
Focused on algebras graded by abelian groups of order ≤8
Abstract
We study not necessarily associative (NNA) division algebras over the reals. We classify in this paper series those that admit a grading over a finite group , and have a basis as a real vector space, and the product of these basis elements respects the grading and includes a scalar structure constant with values only in . We classify here those graded by an abelian group of order with non--isomorphic to . We will find the complex, quaternion, and octonion algebras, but also a remarkable set of novel non--associative division algebras.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic and Geometric Analysis · Algebraic structures and combinatorial models
