The Truncation Algebras Of C~r E Extensions Of One Class Of Skew Group Algebras

In the paper, we construct the C~rE extensions G SL(3,C) of cyclicsubgroup N of SL(2,C),|N|=n+1. And we study the skew group algebraproperties of their tilting modules.In chapter2, we introduce some preliminary knowledge, recall the definitionsof McKay quiver and skew group algebra and recall some properties of one-pointextension as well.In chapter3, we mainly construct the C~rE extensions and truncations ofMcKay quiver of type Anand the special truncation quiver as well.In chapter4, we show some properties of special truncation algebra, we showthat any special truncation algebra of the same quiver are isomorphism, and ifthe total truncation quiver have3components, the trivial extension of specialtruncation algebra isomorphic to the original skew group algebra. We also showthat the AR-quiver of special truncation algebra have only one preprojective com-ponent and only one postinjective component, and the regular components andquasi-regular components separate the preprojective component from postinjec-tive component. And, at the same time, we prove that the special truncationalgebras do not preserve τ-complexity and infinite if the dimension of k-vectorspace V great or equal to3.In chapter5, We prove that there exist tilting modules with direct sums lie inregular and quasi-regular component, and in the last, we discuss some propertiesof tilting theory.