2015/05/13 by Adrian Ocneanu, Ocneanu, Adrian
Computer Science · Mathematics · #Cellular Automata and Applications #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Representation Theory (math.RT) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1505.03248
openalex publication_date 2015/05/13 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
The 4-simplex has vertices 5 unit quaternions, which we arrange so that one\nof them is the unit. We show that the remaining 4 vertices are the generators\nof a free group.\n For the proof, we introduce a new alternating length on words in free groups.\nWe show that for words in simplex vertices the necklace form of the alternating\nlength can be read number theoretically, as the logarithm of the algebraic\ndenominator of their trace.\n