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We study the four infinite families KA(n), KB(n), KD(n), KQ(n) of finite dimensional Hopf (in fact Kac) algebras constructed respectively by A. Masuoka and L. Vainerman: isomorphisms, automorphism groups, self-duality, lattices of coideal subalgebras. We reduce the study to KD(n) by proving that the others are isomorphic to KD(n), its dual, or an index 2 subalgebra of KD(2n). We derive many examples of lattices of intermediate subfactors of the inclusions of depth 2 associated to those Kac algebras, as well as the corresponding principal graphs, which is the original motivation. Along the way, we extend some general results on the Galois correspondence for depth 2 inclusions, and develop some tools and algorithms for the study of twisted group algebras and their lattices of coideal subalgebras. This research was driven by heavy computer exploration, whose tools and methodology we further describe.
We extend Schaumanns theory of pivotal structures on fusion categories matched to a module category and of module traces developed in arXiv:1206.5716 to the case of non-semisimple tensor categories, and use it to study eigenvalues of the squared anti
This is an expository introduction to fusion rules for affine Kac-Moody algebras, with major focus on the algorithmic aspects of their computation and the relationship with tensor product decompositions. Many explicit examples are included with figur
In this paper, we continue the study on toroidal vertex algebras initiated in cite{LTW}, to study concrete toroidal vertex algebras associated to toroidal Lie algebra $L_{r}(hat{frak{g}})=hat{frak{g}}otimes L_r$, where $hat{frak{g}}$ is an untwisted
For a finite-index $mathrm{II}_1$ subfactor $N subset M$, we prove the existence of a universal Hopf $ast$-algebra (or, a discrete quantum group in the analytic language) acting on $M$ in a trace-preserving fashion and fixing $N$ pointwise. We call t
The notion of index for inclusions of von Neumann algebras goes back to a seminal work of Jones on subfactors of type ${I!I}_1$. In the absence of a trace, one can still define the index of a conditional expectation associated to a subfactor and look