Tilting Modules Of Duplicated Algebra And Their Applications

Assume A is a finite dimensional hereditary algebra over an algebraically closed field. Let A(1) denotes the duplicated algebra of A. The article researches some properties of the endomorphism algebra of duplicated algebra tilting modules and gains a result that the tilting quiver of A can be embedded into the tiling quiver of A(1).There are two parts in the article. In the first part, results are followingLet A be a hereditary algebra, all the endomorphism algebras of duplicated algebra tilting modules are finite representation type if and only if A is An type and n is no more than 4.The global dimension of endomorphism algebras of duplicated algebra tilting modules is no more than 3.In the second part, the main result is followingThe tilting quiver of A can be embedded into the tiling quiver of A(1) keeping points and arrows the same. And in the tiling quiver of A(1) the number of arrows connected to a point is equal to the number of simple modules of A.Using this result, the author gives new brief proofs and comprehension to some important theorems in hereditary torsion theory. And the author gives a short proof to a tilting quiver arrows number counting theorem.