2011/05/16 by Guopeng Wang, Wang, Guopeng, Shunhua Zhang +1
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum many-body systems #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.1105.2994
openalex publication_date 2011/05/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let A be a finite dimensional hereditary algebra over a field k and A(1) the duplicated algebra of A. We first show that the global dimension of endomorphism ring of tilting modules of A(1) is at most 3. Then we investigate embedding tilting quiver \mathscrK(A) of A into tilting quiver \mathscrK(A(1)) of A(1). As applications, we give new proofs for some results of D.Happel and L.Unger, and prove that every connected component in \mathscrK(A) has finite non-saturated points if A is tame type, which gives a partially positive answer to the conjecture of D.Happel and L.Unger in [10]. Finally, we also prove that the number of arrows in \mathscrK(A) is a constant which does not depend on the orientation of Q if Q is Dynkin type.