论文标题
降低通用包络代数的块亚代代代代数的过滤
Filtrations on block subalgebras of reduced universal enveloping algebras
论文作者
论文摘要
我们研究了阳性特征，PBW过滤和Nilpotent锥体减少通用代数的块分解之间的相互作用。我们在块subalgebra $a_λ$上提供了两个自然版本的PBW过滤，该限制了通用包络代数$ \ Mathcal {u}_χ（\ Mathfrak {g}）$，并显示这些彼此双重。我们还考虑了一个转移的PBW过滤，我们将相关的分级代数与Frobenius邻域的函数代数相关联，而Nilpotent圆锥中的$ 0 $和Coinvariants代数对应于$λ$。如果是$ \ mathfrak {g} = \ mathfrak {sl} _2（k）$ p> 2 $，我们确定这些过滤的相关分级代数在$ \ mathcal {u} _0（u} _0（\ mathfrak {sl sl} _2 _2 _2）_2）上的block subalgebras上。我们还将其应用于确定$ \ mathcal {u} _0（\ Mathfrak {sl} _2）$的伴随表示的结构。
We study the interaction between the block decompositions of reduced universal enveloping algebras in positive characteristic, the PBW filtration, and the nilpotent cone. We provide two natural versions of the PBW filtration on the block subalgebra $A_λ$ of the restricted universal enveloping algebra $\mathcal{U}_χ(\mathfrak{g})$ and show these are dual to each other. We also consider a shifted PBW filtration for which we relate the associated graded algebra to the algebra of functions on the Frobenius neighbourhood of $0$ in the nilpotent cone and the coinvariants algebra corresponding to $λ$. In the case of $\mathfrak{g}=\mathfrak{sl}_2(k)$ in characteristic $p>2$ we determine the associated graded algebras of these filtrations on block subalgebras of $\mathcal{U}_0(\mathfrak{sl}_2)$. We also apply this to determine the structure of the adjoint representation of $\mathcal{U}_0(\mathfrak{sl}_2)$.
