Exact Borel subalgebras, idempotent quotients and idempotent subalgebras
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914459682865152 |
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| author | Conde, Teresa Külshammer, Julian |
| author_facet | Conde, Teresa Külshammer, Julian |
| contents | This article studies the compatibility of Koenig's notion of an exact Borel subalgebra of a quasi-hereditary or, more generally, standardly stratified algebra with taking idempotent subalgebras or quotients. As an application, we provide bounds for the multiplicities of indecomposable projectives in the principal blocks of BGG category $\mathcal{O}$ having basic regular exact Borel subalgebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_10461 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exact Borel subalgebras, idempotent quotients and idempotent subalgebras Conde, Teresa Külshammer, Julian Representation Theory Rings and Algebras 16G10, 16D90, 16W70, 17B10 This article studies the compatibility of Koenig's notion of an exact Borel subalgebra of a quasi-hereditary or, more generally, standardly stratified algebra with taking idempotent subalgebras or quotients. As an application, we provide bounds for the multiplicities of indecomposable projectives in the principal blocks of BGG category $\mathcal{O}$ having basic regular exact Borel subalgebras. |
| title | Exact Borel subalgebras, idempotent quotients and idempotent subalgebras |
| topic | Representation Theory Rings and Algebras 16G10, 16D90, 16W70, 17B10 |
| url | https://arxiv.org/abs/2503.10461 |