论文标题
准鞘内结构的连接性
Connectedness of quasi-hereditary structures
论文作者
论文摘要
DLAB和RINGEL表明，在所有命令中，代数为原始的dive子索引的代数是遗传性的。因此，我们对给定的准标准代数的命令再次具有准族主管感兴趣。实际上，我们考虑索引的排列，如果带有置换索引的代数为准遗传性，那么我们说这种置换会提供准隐式结构。在本文中，我们首先要根据给定准赫德代数的标准或costandard模块的同源条件，对邻近的换位标准，从而给予准内生性结构。接下来，我们考虑那些我们称之为准主结构的联系。连接性的定义可以在定义4.1中找到。然后，我们证明连接了任何两个准雌性结构，这是我们的主要结果。通过这个结果，一旦我们知道有两个准内生性结构，那么在某种意义上说，置于它们之间的排列也会给出准文生结构。
Dlab and Ringel showed that algebras being quasi-hereditary in all orders for indices of primitive idempotents becomes hereditary. So, we are interested in for which orders a given quasi-hereditary algebra is again quasi-hereditary. As a matter of fact, we consider permutations of indices, and if the algebra with permuted indices is quasi-hereditary, then we say that this permutation gives a quasi-hereditary structure. In this article, we first give a criterion for adjacent transpositions giving quasi-hereditary structures, in terms of homological conditions of standard or costandard modules over a given quasi-hereditary algebra. Next, we consider those which we call connectedness of quasihereditary structures. The definition of connectedness can be found in Definition 4.1. We then show that any two quasi-hereditary structures are connected, which is our main result. By this result, once we know that there are two quasi-hereditary structures, then permutations in some sense lying between them give also quasi-hereditary structures.
