538 research outputs found
Tame concealed algebras and cluster quivers of minimal infinite type
In this paper we explain how and why the list of Happel-Vossieck of tame
concealed algebras is closely related to the list of A. Seven of minimal
infinite cluster quivers.Comment: 16 pages, new version with an additional section on cluster-tilted
algebras of minimal infinite typ
Cluster structures for 2-Calabi-Yau categories and unipotent groups
We investigate cluster tilting objects (and subcategories) in triangulated
2-Calabi-Yau categories and related categories. In particular we construct a
new class of such categories related to preprojective algebras of non Dynkin
quivers associated with elements in the Coxeter group. This class of
2-Calabi-Yau categories contains the cluster categories and the stable
categories of preprojective algebras of Dynkin graphs as special cases. For
these 2-Calabi-Yau categories we construct cluster tilting objects associated
with each reduced expression. The associated quiver is described in terms of
the reduced expression. Motivated by the theory of cluster algebras, we
formulate the notions of (weak) cluster structure and substructure, and give
several illustrations of these concepts. We give applications to cluster
algebras and subcluster algebras related to unipotent groups, both in the
Dynkin and non Dynkin case.Comment: 49 pages. For the third version the presentation is revised,
especially Chapter III replaces the old Chapter III and I
Derived equivalence classification of the cluster-tilted algebras of Dynkin type E
We obtain a complete derived equivalence classification of the cluster-tilted
algebras of Dynkin type E. There are 67, 416, 1574 algebras in types E6, E7 and
E8 which turn out to fall into 6, 14, 15 derived equivalence classes,
respectively. This classification can be achieved computationally and we
outline an algorithm which has been implemented to carry out this task. We also
make the classification explicit by giving standard forms for each derived
equivalence class as well as complete lists of the algebras contained in each
class; as these lists are quite long they are provided as supplementary
material to this paper. From a structural point of view the remarkable outcome
of our classification is that two cluster-tilted algebras of Dynkin type E are
derived equivalent if and only if their Cartan matrices represent equivalent
bilinear forms over the integers which in turn happens if and only if the two
algebras are connected by a sequence of "good" mutations. This is reminiscent
of the derived equivalence classification of cluster-tilted algebras of Dynkin
type A, but quite different from the situation in Dynkin type D where a
far-reaching classification has been obtained using similar methods as in the
present paper but some very subtle questions are still open.Comment: 19 pages. v4: completely rewritten version, to appear in Algebr.
Represent. Theory. v3: Main theorem strengthened by including "good"
mutations (cf. also arXiv:1001.4765). Minor editorial changes. v2: Third
author added. Major revision. All questions left open in the earlier version
by the first two authors are now settled in v2 and the derived equivalence
classification is completed. arXiv admin note: some text overlap with
arXiv:1012.466
Silted algebras
We study endomorphism algebras of 2-term silting complexes in derived
categories of hereditary finite dimensional algebras, or more generally of
-finite hereditary abelian categories. Module
categories of such endomorphism algebras are known to occur as hearts of
certain bounded -structures in such derived categories. We show that the
algebras occurring are exactly the algebras of small homological dimension,
which are algebras characterized by the property that each indecomposable
module either has injective dimension at most one, or it has projective
dimension at most one.Comment: Fix some typos, to appear in Adv. Mat
Physiological Evidence for Isopotential Tunneling in the Electron Transport Chain of Methane-Producing Archaea
Many, but not all, organisms use quinones to conserve energy in their electron transport chains. Fermentative bacteria and methane-producing archaea (methanogens) do not produce quinones but have devised other ways to generate ATP. Methanophenazine (MPh) is a unique membrane electron carrier found in Methanosarcina species that plays the same role as quinones in the electron transport chain. To extend the analogy between quinones and MPh, we compared the MPh pool sizes between two well-studied Methanosarcina species, Methanosarcina acetivorans C2A and Methanosarcina barkeri Fusaro, to the quinone pool size in the bacterium Escherichia coli. We found the quantity of MPh per cell increases as cultures transition from exponential growth to stationary phase, and absolute quantities of MPh were 3-fold higher in M. acetivorans than in M. barkeri. The concentration of MPh suggests the cell membrane of M. acetivorans, but not of M. barkeri, is electrically quantized as if it were a single conductive metal sheet and near optimal for rate of electron transport. Similarly, stationary (but not exponentially growing) E. coli cells also have electrically quantized membranes on the basis of quinone content. Consistent with our hypothesis, we demonstrated that the exogenous addition of phenazine increases the growth rate of M. barkeri three times that of M. acetivorans. Our work suggests electron flux through MPh is naturally higher in M. acetivorans than in M. barkeri and that hydrogen cycling is less efficient at conserving energy than scalar proton translocation using MPh
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