On diagram algebras

本研究旨在对q-壁Brauer代数进行“分类”。我们发现，虽然这个代数是非常复杂的，它的应用将非常有限。因此，我们将研究对象稍作改变，开始研究Khovanov图代数和Motzkin代数。我们还没有成功的“范畴化”Khovanov的代数。然而，我们已经成功地定义了Motzkin代数的定义关系。Khovanov代数将成为联系拓扑对象和代数对象的重要工具。

This research was intended to "Categorify" the q-walled Brauer algebra. We found that although this algebra is very complicated, the application of it would be very limited. So we have changed the research object slightly and began to study Khovanov's diagram algebra and Motzkin algebra. We have not yet succeeded the "Categorification" of Khovanov's algebra. However we have succeeded to define the defining relation go the Motzkin algebra. Khovanov algebra will become an important tool which binds topological objects and algebraic objects.