Highest weight theory for finite-dimensional graded algebras with triangular decomposition
Highest weight theory for finite-dimensional graded algebras with triangular decomposition
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DOI：
10.1016/j.aim.2018.03.011
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发表时间：
2017-05
期刊：
影响因子：
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通讯作者：
G. Bellamy;U. Thiel
中科院分区：
文献类型：
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作者：
G. Bellamy;U. Thiel
证明了具有三角分解的有限维渐变代数上的渐变模范畴可以被赋予最高权范畴的结构。当代数是自内射时，我们进一步证明了这个权重最高的范畴在Ringel意义上具有倾斜模。这为这些代数的表示理论提供了一个新的视角，并导致了一些新的结构附加到它们上。在代数李理论中有各种各样的例子可以应用：受限包络代数、Lusztig小量子群、超代数、有限量子群和受限有理Cherednik代数。
We show that the category of graded modules over a finite-dimensional graded algebra admitting a triangular decomposition can be endowed with the structure of a highest weight category. When the algebra is self-injective, we show furthermore that this highest weight category has tilting modules in the sense of Ringel. This provides a new perspective on the representation theory of such algebras, and leads to several new structures attached to them. There are a wide variety of examples in algebraic Lie theory to which this applies: restricted enveloping algebras, Lusztig's small quantum groups, hyperalgebras, finite quantum groups, and restricted rational Cherednik algebras.