Exceptional Sequences Determined by their Cartan Matrix |
| |
Authors: | Helmut Lenzing Hagen Meltzer |
| |
Institution: | (1) Fachbereich Mathematik-Informatik, Universität-GH Paderborn, D-33095 Paderborn, Germany |
| |
Abstract: | We investigate complete exceptional sequences E=(E
1,¨,E
n
) in the derived category D
b
of finite-dimensional modules over a canonical algebra, equivalently in the derived category D
b
X of coherent sheaves on a weighted projective line, and the associated Cartan matrices C(E)=( E
i
],E
j
]). As a consequence of the transitivity of the braid group action on such sequences we show that a given Cartan matrix has at most finitely many realizations by an exceptional sequence E, up to an automorphism and a multi-translation (E
1,¨,E
n
)(E
1i
1],¨,E
n
i
n
]) of D
b
. Moreover, we determine a bound on the number of such realizations. Our results imply that a derived canonical algebra A is determined by its Cartan matrix up to isomorphism if and only if the Hochschild cohomology of A vanishes in nonzero degree, a condition satisfied if A is representation-finite. |
| |
Keywords: | exceptional sequence tilting complex derived equivalence canonical algebra weighted projective line |
本文献已被 SpringerLink 等数据库收录! |
|