Tensor Triangular Geometry for Quantum Groups

2017/02/04 by Brian D. Boe, Boe, Brian D., Jonathan R. Kujawa +3 · 1 citation
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Noncommutative and Quantum Gravity Theories

paper · pdf · doi:10.48550/arxiv.1702.01289

Abstract

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

Cited by

• Tensor ideals of abelian type and quantum groups

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