Algebras from surfaces without punctures

作者：David Roesler Lucas; Schiffler Ralf^*

来源：Journal of Algebra, 2012, 350(1): 218-244.

DOI：10.1016/j.jalgebra.2011.10.034

• Gentle algebra
• Tilting theory
• Bordered surface with marked points
• Derived equivalence

We introduce a new class of finite-dimensional gentle algebras, the surface algebras, which are constructed from an unpunctured Riemann surface with boundary and marked points by introducing cuts in internal triangles of an arbitrary triangulation of the surface. We show that surface algebras are endomorphism algebras of partial cluster-tilting objects in generalized cluster categories, we compute the invariant of Avella-Alaminos and Geiss for surface algebras and we provide a geometric model for the module category of surface algebras.

• 出版日期2012-1-15