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Full-Text Articles in Mathematics
Albert Forms, Quaternions, Schubert Varieties & Embeddability, Jasmin Omanovic
Albert Forms, Quaternions, Schubert Varieties & Embeddability, Jasmin Omanovic
Electronic Thesis and Dissertation Repository
The origin of embedding problems can be understood as an effort to find some minimal datum which describes certain algebraic or geometric objects. In the algebraic theory of quadratic forms, Pfister forms are studied for a litany of powerful properties and representations which make them particularly interesting to study in terms of embeddability. A generalization of these properties is captured by the study of central simple algebras carrying involutions, where we may characterize the involution by the existence of particular elements in the algebra. Extending this idea even further, embeddings are just flags in the Grassmannian, meaning that their study …
Mirror Symmetry For Non-Abelian Landau-Ginzburg Models, Matthew Michael Williams
Mirror Symmetry For Non-Abelian Landau-Ginzburg Models, Matthew Michael Williams
Theses and Dissertations
We consider Landau-Ginzburg models stemming from non-abelian groups comprised of non-diagonal symmetries, and we describe a rule for the mirror LG model. In particular, we present the non-abelian dual group G*, which serves as the appropriate choice of group for the mirror LG model. We also describe an explicit mirror map between the A-model and the B-model state spaces for two examples. Further, we prove that this mirror map is an isomorphism between the untwisted broad sectors and the narrow diagonal sectors in general.