Quasi-hereditary algebras, exact Borel subalgebras, A-infinity-categories and boxes
Quasi-hereditary algebras, exact Borel subalgebras, A-infinity-categories and boxes
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准遗传代数、精确 Borel 子代数、A-无穷范畴和盒子
DOI：
10.1016/j.aim.2014.05.016
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
S. Ovsienko
中科院分区：
文献类型：
--
作者：
S. Koenig;Julian Kulshammer;S. Ovsienko
李论中出现的最高权范畴通常与有限维拟遗传代数有关，如Schur代数或O类的块。PBW定理的类比将被证明适用于拟遗传代数：直到Morita等价，每个此类代数都有一个精确的Borel子代数。具有标准的(Verma，Weyl，Δ)模的范畴F(…)过滤是精确的，但很少是阿贝尔的，它将被证明等同于有向盒子的表示范畴。这个盒子被构造为与Ext∞上的A⁎(Δ，Δ结构相关联的dg代数的商)。它的基础代数是精确的Borel子代数。
Highest weight categories arising in Lie theory are known to be associated with finite dimensional quasi-hereditary algebras such as Schur algebras or blocks of category O. An analogue of the PBW theorem will be shown to hold for quasi-hereditary algebras: Up to Morita equivalence each such algebra has an exact Borel subalgebra. The category F (Δ) of modules with standard (Verma, Weyl,…) filtration, which is exact, but rarely abelian, will be shown to be equivalent to the category of representations of a directed box. This box is constructed as a quotient of a dg algebra associated with the A∞-structure on Ext⁎(Δ, Δ). Its underlying algebra is an exact Borel subalgebra.