论文标题
$ sl_3 $ skein代数的三角分解
Triangular decomposition of $SL_3$ skein algebras
论文作者
论文摘要
我们给出了$ sl_3 $的类似物的类似物的三角形分解，kauffman支架表示LE所描述的Kkein代数。对于任何被刺穿的边界表面，我们将$ sl_3 $陈述的Skein代数包含$ sl_3 $ skein代数的封闭网。这些代数接受与理想弧沿表面分裂相关的自然代数形态。我们为$ sl_3 $陈述的绞线代数给出了明确的基础，并表明分裂的形态是注入性的，并描述了它们的图像。通过沿理想三角剖分的边缘拆分表面，我们看到$ sl_3 $表示的任何理想的三角形表面的绞线代数都嵌入了三角形的规定绞线代数的张量产品中。
We give an $SL_3$ analogue of the triangular decomposition of the Kauffman bracket stated skein algebras described by Le. To any punctured bordered surface, we associate an $SL_3$ stated skein algebra which contains the $SL_3$ skein algebra of closed webs. These algebras admit natural algebra morphisms associated to the splitting of surfaces along ideal arcs. We give an explicit basis for the $SL_3$ stated skein algebra and show that the splitting morphisms are injective and describe their images. By splitting a surface along the edges of an ideal triangulation, we see that the $SL_3$ stated skein algebra of any ideal triangulable surface embeds into a tensor product of stated skein algebras of triangles.
