2015/04/24 by Marc Sauerwein
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Dihedral angle #Dihedral group #Dual (grammatical number) #Duality (order theory) #Endomorphism #Generator (circuit theory) #Group (periodic table) #Hydrogen bond #Linguistics #Mathematics #Power (physics) #Pure mathematics #Ring (chemistry) #math.QA #math.RT #msc:16S37
paper · pdf · doi:10.1090/tran/7014
published as Trans. Amer. Math. Soc. 370 (2018), 1251-1283 · 29 pages
arxiv created 2015/04/24 · openalex publication_date 2016/07/14 · arxiv updated 2017/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Every Coxeter system (W,S) gives rise to a Hecke algebra \textbf H (W,S) which can be categorified by the additive monoidal category of Soergel bimodules \mathcal S\mathcal B. Under this isomorphism the Kazhdan-Lusztig basis \\underline Hx\x∈ W corresponds to certain indecomposable Soergel bimodules \Bx\x∈ W (up to shift). In this thesis we study the structure of the endomorphism algebra (of maps of all degrees) \mathcal A:= \operatorname End^\bullet \mathcal S\mathcal B (\bigoplus x∈ W Bx )⊗ R\mathbb R. Via category \mathcal O it has been proven for all Weyl groups that \mathcal A is a self-dual Koszul algebra. We extend this result to all dihedral groups by purely algebraic methods using representation theory of quivers and Soergel calculus.