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Izv. RAN. Ser. Mat., 2017, Volume 81, Issue 4, Pages 158–166 (Mi izv8620)  

This article is cited in 4 scientific papers (total in 4 papers)

Grothendieck–Verdier duality patterns in quantum algebra

Yu. I. Manin

Max Planck Institute for Mathematics

Abstract: After a brief survey of the basic definitions of Grothendieck–Verdier categories and dualities, I consider in this context dualities introduced earlier 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 must also fit a (possibly extended) version of Grothendieck–Verdier duality.

Keywords: duality, $F$-manifolds, quadratic algebras, quadratic operads.

DOI: https://doi.org/10.4213/im8620

Full text: PDF file (424 kB)
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English version:
Izvestiya: Mathematics, 2017, 81:4, 818–826

Bibliographic databases:

UDC: 512.581+512.664
MSC: 18D10, 16S37, 18G35
Received: 25.10.2016
Revised: 25.12.2016
Language:

Citation: Yu. I. Manin, “Grothendieck–Verdier duality patterns in quantum algebra”, Izv. RAN. Ser. Mat., 81:4 (2017), 158–166; Izv. Math., 81:4 (2017), 818–826

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. Dotsenko, “Algebraic structures of $F$ -manifolds via pre-lie algebras”, Ann. Mat. Pura Appl. (4), 198:2 (2019), 517–527  crossref  mathscinet  zmath  isi  scopus
    2. J. A. Cruz Morales, A. Torres-Gomez, “On f-algebroids and Dubrovin's duality”, Arch. Math. (Brno), 55:2 (2019), 109–122  crossref  mathscinet  zmath  isi  scopus
    3. Yu. I. Manin, “Higher structures, quantum groups and genus zero modular operad”, J. Lond. Math. Soc.-Second Ser., 100:3 (2019), 721–730  crossref  mathscinet  zmath  isi  scopus
    4. J. F&quot, G. Schaumann, Ch. Schweigert, “Eilenberg-watts calculus for finite categories and a bimodule Radford $S^4$ theorem”, Trans. Amer. Math. Soc., 373:1 (2020), 1–40  crossref  mathscinet  zmath  isi  scopus
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