2011/04/01 by Angela Klamt, Klamt, Angela · 3 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT) #math.CT #math.RT
paper · pdf · doi:10.48550/arxiv.1104.0102
arxiv created 2011/04/01 · openalex publication_date 2011/04/01 · arxiv updated 2011/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This is the author's diploma thesis. In the first part of the thesis the algebra structure on the Ext-spaces Extk(M(x), M(y)) of Verma modules M(x) and M(y) in the parabolic category O for the case of the parabolic subalgebras gl(n) x gl(m) for n=1 and n=2 is computed and expressed in terms of quivers. For arbitrary n, more general results about Hom-spaces of projective modules are achieved. The second part of the thesis deals with A-infinity structures on the algebras described above. An explicit construction for a minimal model is given and all higher multiplications are determined in the cases n=1 and n=2. In the first case the algebra turns out to be formal. The main result of the thesis is presented in the general vanishing theorem. It says that for arbitrary n we get a minimal model with vanishing mk for k > n2+1. The tools used for this proof are developed throughout the entire thesis.