13 citations · 54 across the 21 of their papers we have counts for
10 papers · 1 filter
Revisiting the Steinberg representation at arbitrary roots of 1
Cris Negron
We consider quantum group representations for a semisimple algebraic group G at a complex root of unity q. Here q is allowed to be of any order. We revisit some fundamental results…
The half-quantum flag variety and representations for small quantum groups
Cris Negron, Julia Pevtsova
Consider an almost-simple algebraic group G and a choice of complex root of unity q. We study the category of quasi-coherent sheaves on the half-quantum flag variet…
Support theory for the small quantum group and the Springer resolution
Cris Negron, Julia Pevtsova
We consider the small quantum group u_q(G), for an almost-simple algebraic group G over the complex numbers and a root of unity q of sufficiently large order. We show that the Balm…
Support theory for Drinfeld doubles of some infinitesimal group schemes
Eric M. Friedlander, Cris Negron
Consider a Frobenius kernel G in a split semisimple algebraic group, in very good characteristic. We provide an analysis of support for the Drinfeld center Z(rep(G)) of the represe…
Hypersurface support and prime ideal spectra for stable categories
Cris Negron, Julia Pevtsova
We use hypersurface support to classify thick (two-sided) ideals in the stable categories of representations for several families of finite-dimensional integrable Hopf algebras: bo…
Support for integrable Hopf algebras via noncommutative hypersurfaces
Cris Negron, Julia Pevtsova
We consider finite-dimensional Hopf algebras which admit a smooth deformation by a Noetherian Hopf algebra of finite global dimension. Examples of such Hopf algebr…
-coderivations and the Gerstenhaber bracket on Hochschild cohomology
C. Negron, Y. Volkov, S. Witherspoon
We show that Hochschild cohomology of an algebra over a field is a space of infinity coderivations on an arbitrary projective bimodule resolution of the algebra. The Gerstenhaber b…
Cohomology for Drinfeld doubles of some infinitesimal group schemes
Eric Friedlander, Cris Negron
Consider a field k of characteristic p > 0, G_r the r-th Frobenius kernel of a smooth algebraic group G, DG_r the Drinfeld double of G_r, and M a finite dimensional DG_r-module. We…
Small quantum groups associated to Belavin-Drinfeld triples
Cris Negron
For a simple Lie algebra L of type A, D, E we show that any Belavin-Drinfeld triple on the Dynkin diagram of L produces a collection of Drinfeld twists for Lusztig's small quantum…
An Alternate Approach to the Lie Bracket on Hochschild Cohomology
Cris Negron, Sarah Witherspoon
We define Gerstenhaber's graded Lie bracket directly on complexes other than the bar complex, under some conditions. The Koszul complex of a Koszul algebra in particular satisfies…