45,411 research outputs found
Resolutions of mesh algebras: periodicity and Calabi-Yau dimensions
A triangulated category is said to be Calabi-Yau of dimension d if the dth
power of its suspension is a Serre functor. We determine which stable
categories of self-injective algebras A of finite representation type are
Calabi-Yau and compute their Calabi-Yau dimensions. We achieve this by studying
the minimal projective resolution of the stable Auslander algebra of A over its
enveloping algebra, and use covering theory to reduce to (generalized)
preprojective algebras of Dynkin graphs. We also describe how this problem can
be approached by realizing the stable categories in question as orbit
categories of the bounded derived categories of hereditary algebras.Comment: Final version. To appear in Math.
On the algorithmic construction of classifying spaces and the isomorphism problem for biautomatic groups
We show that the isomorphism problem is solvable in the class of central
extensions of word-hyperbolic groups, and that the isomorphism problem for
biautomatic groups reduces to that for biautomatic groups with finite centre.
We describe an algorithm that, given an arbitrary finite presentation of an
automatic group , will construct explicit finite models for the skeleta
of and hence compute the integral homology and cohomology of
.Comment: 21 pages, 4 figure
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