Universal deformation rings of modules for algebras of dihedral type of polynomial growth

Let k be an algebraically closed field, and let \Lambda\ be an algebra of dihedral type of polynomial growth as classified by Erdmann and Skowro\'{n}ski. We describe all finitely generated \Lambda-modules V whose stable endomorphism rings are isomorphic to k and determine their universal deformation rings R(\Lambda,V). We prove that only three isomorphism types occur for R(\Lambda,V): k, k[[t]]/(t^2) and k[[t]].Comment: 11 pages, 2 figure

Infinitely many N=2 SCFT with ADE flavor symmetry

We present evidence that for each ADE Lie group G there is an infinite tower of 4D N = 2 SCFTs, which we label as D(G, s) with s 08 \u2115, having (at least) flavor symmetry G. For G = SU(2), D(SU(2),s) coincides with the Argyres-Douglas model of type D8+1, while for larger flavor groups the models are new (but for a few previously known examples). When its flavor symmetry G is gauged, D(G,s) contributes to the Yang-Mills beta-function as 8/2(+1) adjoint hypermultiplets. The argument is based on a combination of Type IIB geometric engineering and the categorical deconstruction of arXiv: 1203.6743. One first engineers a class of N = 2 models which, trough the analysis of their category of quiver representations, are identified as asymptotically-free gauge theories with gauge group G coupled to some conformal matter system. Taking the limit gYM \u2192 0 one isolates the matter SCFT which is our D(G, s). \ua9 SISSA 2013

4d N=2 Gauge Theories and Quivers: the Non-Simply Laced Case

We construct the BPS quivers with superpotential for the 4d N=2 gauge theories with non-simply laced Lie groups (B_n, C_n, F_4 and G_2). The construction is inspired by the BIKMSV geometric engineering of these gauge groups as non-split singular elliptic fibrations. From the categorical viewpoint of arXiv:1203.6743, the fibration of the light category L(g) over the (degenerate) Gaiotto curve has a monodromy given by the action of the outer automorphism of the corresponding unfolded Lie algebra. In view of the Katz--Vafa `matter from geometry' mechanism, the monodromic idea may be extended to the construction of (Q, W) for SYM coupled to higher matter representations. This is done through a construction we call specialization.Comment: 42 pages, 2 figure

Discrete derived categories I: homomorphisms, autoequivalences and t-structures

Discrete derived categories were studied initially by Vossieck (J Algebra 243:168–176, 2001) and later by Bobiński et al. (Cent Eur J Math 2:19–49, 2004). In this article, we describe the homomorphism hammocks and autoequivalences on these categories. We classify silting objects and bounded t-structures