81 citations · 318 across the 48 of their papers we have counts for
5 papers · 1 filter
Grothendieck-Verdier duality patterns in quantum algebra
Yuri I. Manin
After a brief survey of the basic definitions of the Grothendieck--Verdier categories and dualities, I consider in this context introduced earlier dualities in the categories of qu…
Quantum theta functions and Gabor frames for modulation spaces
Franz Luef, Yuri I. Manin
Representations of the celebrated Heisenberg commutation relations in quantum mechanics and their exponentiated versions form the starting point for a number of basic constructions…
Functional equations for quantum theta functions
Yu. I. Manin
Quantum theta functions were introduced by the author in [Ma1]. They are certain elements in the function rings of quantum tori. By definition, they satisfy a version of the classi…
Weak Frobenius manifolds
Claus Hertling, Yuri Manin
We establish a new universal relation between the Lie bracket and -multiplication of tangent fields on any Frobenius (super)manifold. We use this identity in order to introd…
Three constructions of Frobenius manifolds: a comparative study
Yu. I. Manin
The paper studies three classes of Frobenius manifolds: Quantum Cohomology (topological sigma-models), unfolding spaces of singularities (K. Saito's theory, Landau-Ginzburg models)…