کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4585424 | 1630542 | 2012 | 12 صفحه PDF | دانلود رایگان |
Let A be a finite dimensional algebra over an algebraically closed field k. Assume A is basic connected with n pairwise non-isomorphic simple modules. We consider the Coxeter polynomial χA(T) of a one-point extension algebra A=B[M] and the polynomial of the extension . If M is exceptional then p(T)=1+p1T+⋯+pn−3Tn−3+Tn−2. In that case, we call s(A:B)=p1 the linear index of the extension A=B[M]. We give conditions for s(A:B)⩾0. For a tower T=(k=A1,A2,…,An=A) of access to A, that is, Ai is a one-point (co-)extension of Ai−1 by an exceptional module, the index , is an invariant depending on the derived equivalence class of A, where a2 is the quadratic coefficient of χA(T). We show that, in the case A is piecewise hereditary, then a2=1 if and only if A is derived equivalent to a quiver algebra of type An.
Journal: Journal of Algebra - Volume 372, 15 December 2012, Pages 149-160