Landau-Ginzburg mirror symmetry predicts isomorphisms between graded Frobenius algebras (denoted A and B ) that are constructed from a nondegenerate quasihomogeneous polynomial W and a related group of symmetries G . Duality between A and B models has been conjectured for particular choices of W and G . These conjectures have been proven in many instances where W is restricted to having the same number of monomials as variables (called \invertible). Some conjectures have been made regarding isomorphisms between A and B models when W is allowed to have more monomials than variables. In this paper we show these conjectures are false; that is, the conjectured isomorphisms do not exist. Insight into this problem will not only generate new results for Landau-Ginzburg mirror symmetry, but will also be interesting from a purely algebraic standpoint as a result about groups acting on graded algebras.
"Transposing Noninvertible Polynomials,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 16:
2, Article 4.
Available at: https://scholar.rose-hulman.edu/rhumj/vol16/iss2/4