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Quantum Frobenius and modularity for quantum groups at arbitrary roots of 1
Cris Negron
We consider quantum group representations Rep(G_q) for a semisimple algebraic group G at a complex root of unity q. Here we allow q to be of any order. We first show that the Tanna…
Quantum SL(2) and logarithmic vertex operator algebras at (p,1)-central charge
Terry Gannon, Cris Negron
We provide a ribbon tensor equivalence between the representation category of small quantum SL(2), at parameter q=exp( i/p), and the representation category of the triplet verte…
Finite generation of cohomology for Drinfeld doubles of finite group schemes
Cris Negron
We prove that the Drinfeld double of an arbitrary finite group scheme has finitely generated cohomology. That is to say, for G any finite group scheme, and D(G) the Drinfeld double…
Log-modular quantum groups at even roots of unity and the quantum Frobenius I
Cris Negron
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-equivar…
Cohomology of finite tensor categories: duality and Drinfeld centers
Cris Negron, Julia Yael Plavnik
We consider the finite generation property for cohomology of a finite tensor category C, which requires that the self-extension algebra of the unit Ext*_C(1,1) is a finitely genera…
Twists of quantum Borel algebras
Cris Negron
We classify Drinfeld twists for the quantum Borel subalgebra u_q(b) in the Frobenius-Lusztig kernel u_q(g), where g is a simple Lie algebra over C and q an odd root of unity. More…