Hilbert Evolution Algebras, Weighted Digraphs, and Nilpotency
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales Serie A, Matemáticas(2024)
摘要
Hilbert evolution algebras generalize evolution algebras through a framework of Hilbert spaces. In this work we focus on infinite-dimensional Hilbert evolution algebras and their representation through a suitably defined weighted digraph. By means of studying such a digraph we obtain new properties for these structures extending well-known results related to the nilpotency of finite dimensional evolution algebras. We show that differently from what happens for the finite dimensional evolution algebras, the notions of nil and nilpotency are not equivalent for Hilbert evolution algebras. Furthermore, we exhibit necessary and sufficient conditions under which a given Hilbert evolution algebra is nil or nilpotent. Our approach includes illustrative examples.
更多查看译文
关键词
Evolution algebra,Hilbert evolution algebra,Nilpotency,Nil,Infinite graph,Hilbert space,17D99,05C25,05C63
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要