Tensor Triangular Geometry for Quantum Groups

Abstract

Let $\mathfrak{g}$ be a complex simple Lie algebra and let $U_{\zeta }(\mathfrak{g})$ be the corresponding Lusztig $\mathbb{Z}[q,q^{-1}]$-form of the quantized enveloping algebra specialized to an $\ell$th root of unity. Moreover, let $\mathrm{mod}(U_{\zeta }(\mathfrak{g}))$ be the braided monoidal category of finite-dimensional modules for $U_{\zeta }(\mathfrak{g})$. In this paper we classify the thick tensor ideals of $\mathrm{mod}(U_{\zeta }(\mathfrak{g}))$ and compute the prime spectrum of the stable module category associated to $\text{mod}(U_{\zeta }(\mathfrak{g}))$ as defined by Balmer.

References in corpus (1)

• Cohomology for quantum groups via the geometry of the nullcone

Cited by in corpus (3)

• Hypersurface support and prime ideal spectra for stable categories
• Balmer spectra and Drinfeld centers
• Derived counterparts of fusion categories of quantum groups