English

Grothendieck-Verdier duality patterns in quantum algebra

Quantum Algebra 2017-10-11 v1

Abstract

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 quadratic algebras and operads, largely motivated by the theory of quantum groups. Finally, I argue that Dubrovin's "almost duality" in the theory of Frobenius manifolds and quantum cohomology also must fit a (possibly extended) version of Grothendieck--Verdier duality.

Keywords

Cite

@article{arxiv.1701.01261,
  title  = {Grothendieck-Verdier duality patterns in quantum algebra},
  author = {Yuri I. Manin},
  journal= {arXiv preprint arXiv:1701.01261},
  year   = {2017}
}

Comments

13 pages, accepted for publication in Izvestiya: Mathematics

R2 v1 2026-06-22T17:41:46.950Z