Uniqueness of exact Borel subalgebras and bocses
| Autor: | Külshammer, Julian, Miemietz, Vanessa |
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| Rok vydání: | 2021 |
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| Druh dokumentu: | Working Paper |
| Popis: | Together with Koenig and Ovsienko, the first author showed that every quasi-hereditary algebra can be obtained as the (left or right) dual of a directed bocs. In this monograph, we prove that if one additionally assumes that the bocs is basic, a notion we define, then this bocs is unique up to isomorphism. This should be seen as a generalisation of the statement that the basic algebra of an arbitrary associative algebra is unique up to isomorphism. The proof associates to a given presentation of the bocs an $A_\infty$-structure on the $\operatorname{Ext}$-algebra of the standard modules of the corresponding quasi-hereditary algebra. Uniqueness then follows from an application of Kadeishvili's theorem. Comment: 71 pages with an appendix of 119 pages |
| Databáze: | arXiv |
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