Algebres de Frobenius-Virasoro

Log-modular quantum groups at even roots of unity and the quantum Frobenius I

We construct log-modular quantum groups at even order roots of unity, both as finite-dimensional ribbon quasi-Hopf algebras and as finite ribbon tensor categories, via a de-equivariantization procedure. The existence of such quantum groups had been predicted by certain conformal field theory considerations, but constructions had not appeared until recently. We show that our quantum groups can be identified with those of Creutzig-Gainutdinov-Runkel in type A_1, and Gainutdinov-Lentner-Ohrmann in arbitrary Dynkin type. We discuss conjectural relations with vertex operator algebras at (1,p)-centr…

$C^*$-张量范畴中的单倍代数与 Schellekens 列表

Haploid algebras in $C^*$-tensor categories and the Schellekens list

本文利用 $C^*$-张量范畴中单倍代数与 Q-系统的刚性等价，证明 Schellekens 列表前 70 个全纯 VOA 的幺正性与强局域性，并分类低中心荷超 Virasoro 扩张。