Strong Exact Borel Subalgebras of Quasi-hereditary Algebras and Abstract Kazhdan–Lusztig Theory
Strong exact Borel subalgebras and strong Δ-subalgebras are shown to exist for quasi-hereditary algebras which possess exact Borel subalgebras and Δ-subalgebras. This implies that the algebras associated with blocks of category O have strong exact Borel subalgebras and strong Δ-subalgebras. The stru...
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| Veröffentlicht in: | Advances in mathematics (New York. 1965) 1999-10, Vol.147 (1), p.110-137 |
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| container_title | Advances in mathematics (New York. 1965) |
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| creator | König, Steffen |
| description | Strong exact Borel subalgebras and strong Δ-subalgebras are shown to exist for quasi-hereditary algebras which possess exact Borel subalgebras and Δ-subalgebras. This implies that the algebras associated with blocks of category O have strong exact Borel subalgebras and strong Δ-subalgebras. The structure of these subalgebras is shown to be closely related to abstract Kazhdan–Lusztig theory. The main technical tool in this paper is a construction which has an exact Borel subalgebras (of a given quasi-hereditary algebra) as input and a strong exact Borel subalgebra as output. From this result, Morita invariance of the existence of exact Borel subalgebras is derived. |
| doi_str_mv | 10.1006/aima.1999.1837 |
| format | Article |
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| title | Strong Exact Borel Subalgebras of Quasi-hereditary Algebras and Abstract Kazhdan–Lusztig Theory |
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