$(k+1)$-potent Matrices in triangular matrix Groups and Incidence Algebras of Finite Posets
| Autor: | Gargate, Ivan, Gargate, Michael |
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| Rok vydání: | 2020 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Let $\mathbb{K}$ be a field such that $char(\mathbb{K})\nmid k$ and $char(\mathbb{K})\nmid k+1$. We describe all $(k+1)$-potent matrices over the group of upper triangular matrix. In the case that $\mathbb{K}$ is a finite field we show how to compute the number of these elements in triangular matrix groups and use this formula to compute the number of $(k+1)$-potent elements in the Incidence Algebra $\mathcal{I}(X,\mathbb{K})$ where $X$ is a finite poset. Comment: 20 pages, 5 figures, 11 tables |
| Databáze: | arXiv |
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