Some Examples Of Silted Algebras Of Dynkin Type

This thesis mainly studies silted algebras over path algebras of Dynkin quivers,namely,endomorphism algebras of 2-term silting complexes.Based on the algorithm of Happel and Ringel which produces tilting modules,we obtain an algorithm to produce all basic 2-term silting complexes.We then apply this algorithm to the paths algebras of certain Dynkin quivers and classify all silted algebras.We notice that in the type A examples all silted algebras are tilted algebras,while in type D there are a few strictly shod algebras,although almost all silted algebras are tilted.In chapter2 we introduce quivers and path algebras,tilting modules,tilted algebras,shod algebras and derived categories,and also introduce some notation.In chapter3 we recall the definition and basic properties of 2-term silting complexes and silted algebras.In chapter4 we will describe an algorithm to produce all basic 2-term silting complexes over the path algebra of a Dynkin quiver,and use this algorithm to compute some examples.