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Sparseness of tstructures and negative Calabi–Yau dimension in triangulated categories generated by a spherical object
 Bull. London Math. Soc., in press
, 2012
"... Abstract. Let k be an algebraically closed field and let T be the klinear algebraic triangulated category generated by a wspherical object for an integer w. For certain values of w this category is classical. For instance, if w = 0 ..."
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Abstract. Let k be an algebraically closed field and let T be the klinear algebraic triangulated category generated by a wspherical object for an integer w. For certain values of w this category is classical. For instance, if w = 0
Coloured quivers for rigid objects and partial triangulations: the unpunctured case
 Proc. Lond. Math. Soc
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SILTING OBJECTS, SIMPLEMINDED COLLECTIONS, tSTRUCTURES AND COtSTRUCTURES FOR FINITEDIMENSIONAL ALGEBRAS
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Categorical tinkertoys for N = 2 gauge theories
"... In view of classification of the quiver 4d N = 2 supersymmetric gauge theories, we discuss the characterization of the quivers with superpotential (Q,W) associated to aN = 2 QFT which, in some corner of its parameter space, looks like a gauge theory with gauge group G. The basic idea is that the Abe ..."
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In view of classification of the quiver 4d N = 2 supersymmetric gauge theories, we discuss the characterization of the quivers with superpotential (Q,W) associated to aN = 2 QFT which, in some corner of its parameter space, looks like a gauge theory with gauge group G. The basic idea is that the Abelian category rep(Q,W) of (finite–dimensional) representations of the Jacobian algebra CQ/(∂W) should enjoy what we call the Ringel property of type G; in particular, rep(Q,W) should contain a universal ‘generic ’ subcategory, which depends only on the gauge group G, capturing the universality of the gauge sector. More precisely, there is a family of ‘light ’ subcategories Lλ ⊂ rep(Q,W), indexed by points λ ∈ N, where N is a projective variety whose irreducible components are copies of P1 in one–to–one correspondence with the simple factors of G. If λ is the generic point of the i–th irreducible component, Lλ is the universal subcategory corresponding to the i–th simple factor of G. Matter, on the contrary, is encoded in the subcategories Lλa where {λa} is a finite set of closed points in N. In particular, for a Gaiotto theory there is one such family of subcategories, Lλ∈N, for each maximal degeneration of the corresponding surface Σ, and the index variety N may be identified with the degenerate Gaiotto surface itself: generic light subcategories correspond to cylinders, while closed–point subcategories to ‘fixtures ’ (spheres with three punctures of various kinds) and higher–order generalizations. The rules for ‘gluing ’ categories are more general that the geometric gluing of surfaces, allowing for a few additional exceptional N = 2 theories which are not of the Gaiotto class. We include several examples and some amusing consequence, as the characterization in terms of quiver combinatorics of asymptotically free theories.