Necessary conditions for the existence of Morita Contexts in the bicategory of Landau-Ginzburg Models

2021/06/19 by Yves Fomatati, Fomatati, Yves
Chemistry · Mathematics · #15A23 #15A69 #16D90 #18N10 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Molecular spectroscopy and chirality #math.CT #msc:15A23 #msc:15A69 #msc:16D90 #msc:18N10

paper · pdf · doi:10.48550/arxiv.2106.10490

23 pages

arxiv created 2021/06/19 · openalex publication_date 2021/06/19 · arxiv updated 2021/06/22 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

We use a matrix approach to study the concept of Morita context in the bicategory LG_K of Landau-Ginzburg models on a particular class of objects. In fact, we first use properties of matrix factorizations to state and prove two necessary conditions to obtain a Morita context between two objects of LG_K. Next, we use a celebrated result (due to Schur) on determinants of block matrices to show that these necessary conditions are not sufficient. Finally, we state a trivial sufficient condition.

Citations

• Matrix factorizations and the Landau-Ginzburg/conformal field theory correspondence
• Introduction to Vector Spaces, Vector Algebras, and Vector Geometries
• Determinants of block matrices

Related

• A note on the bicategory of Landau-Ginzburg models (LGk)
• Global matrix factorizations
• The cut operation on matrix factorisations
• Monoidal Morita equivalence
• Ginzburg-Landau description of a class of non-unitary minimal models