Oriented CW complexes and finite-dimensional alternative algebras. (English) Zbl 1543.17032
Latest trend in Mathematics is finding new links between different fields. This paper deals with the relation between Graph Theory and alternative algebras. The authors provide a mapping between Lie algebras and oriented CW complexes in order to translate properties of Lie algebras into the language of Graph Theory and vice versa. An algorithmic procedure to associate oriented CW complexes with alternative algebras was developed by the authors. The authors probed the structure of (pseudo)digraphs associated with alternative algebras and some of their properties and for each configuration, the type of alternative algebra considering solvability and nilpotency are analyzed. THey also provide a brief computational study, showing the complexity order and computing time of the routines of the algorithm.
Reviewer: V. Yegnanarayanan (Chennai)
MSC:
| 17D05 | Alternative rings |
| 05C25 | Graphs and abstract algebra (groups, rings, fields, etc.) |
| 05C20 | Directed graphs (digraphs), tournaments |
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