The global dimension of the algebra of the monoid of all partial functions on an $n$-set as the algebra of the EI-category of epimorphisms between subsets
| Autor: | Stein, Itamar |
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| Rok vydání: | 2017 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We prove that the global dimension of the complex algebra of the monoid of all partial functions on an n-set is $n-1$ for all $n\geq 1$. This is also the global dimension of the complex algebra of the category of all epimorphisms between subsets of an $n$-set. In our proof we use standard homological methods as well as combinatorial techniques associated to the representation theory of the symmetric group. As part of the proof, we obtain a partial description of the Cartan matrix of these algebras. Comment: 27 pages |
| Databáze: | arXiv |
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