Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.05850 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- In this paper, we introduce a novel generalization of the classical property of algebras known as "being alternative," which we term "partially alternative." This new concept broadens the scope of alternative algebras, offering a fresh perspective on their structural properties. We showed that partially alternative algebras exist in any even dimension. Then we classified middle $\mathbb C$-associative (noncommutative) algebras satisfying partial alternativity condition. We demonstrated that for any four-dimensional partially alternative real division algebra, one can select a basis that significantly simplifies its multiplication table. Furthermore, we established that every four-dimensional partially alternative real division algebra naturally gives rise to a real Lie algebra, thereby bridging these two important algebraic frameworks. Our work culminates in a description of all Lie algebras arising from such partially alternative algebras. These results extend our understanding of algebraic structures and reveal new connections between different types of algebras.