Hilbert evolution algebras, weighted digraphs, and nilpotency
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...
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| Veröffentlicht in: | Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas Físicas y Naturales. Serie A, Matemáticas, 2024-07, Vol.118 (3), Article 117 |
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| container_title | Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas |
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| creator | Cadavid, Paula Rodriguez, Pablo M. Vidal, Sebastian J. |
| description | 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. |
| doi_str_mv | 10.1007/s13398-024-01616-w |
| format | Article |
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| ispartof | Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas, 2024-07, Vol.118 (3), Article 117 |
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| language | eng |
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| subjects | Algebra Applications of Mathematics Evolution Graph theory Hilbert space Mathematical and Computational Physics Mathematics Mathematics and Statistics Original Paper Theoretical |
| title | Hilbert evolution algebras, weighted digraphs, and nilpotency |
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