Keywords: F-manifolds; Frobenius manifolds; Lie algebroids
@article{10_5817_AM2019_2_109,
author = {Cruz Morales, John Alexander and Torres-Gomez, Alexander},
title = {On {F-algebroids} and {Dubrovin{\textquoteright}s} duality},
journal = {Archivum mathematicum},
pages = {109--122},
year = {2019},
volume = {55},
number = {2},
doi = {10.5817/AM2019-2-109},
mrnumber = {3964438},
zbl = {07088762},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.5817/AM2019-2-109/}
}
TY - JOUR AU - Cruz Morales, John Alexander AU - Torres-Gomez, Alexander TI - On F-algebroids and Dubrovin’s duality JO - Archivum mathematicum PY - 2019 SP - 109 EP - 122 VL - 55 IS - 2 UR - http://geodesic.mathdoc.fr/articles/10.5817/AM2019-2-109/ DO - 10.5817/AM2019-2-109 LA - en ID - 10_5817_AM2019_2_109 ER -
Cruz Morales, John Alexander; Torres-Gomez, Alexander. On F-algebroids and Dubrovin’s duality. Archivum mathematicum, Tome 55 (2019) no. 2, pp. 109-122. doi: 10.5817/AM2019-2-109
[1] Audin, M.: Symplectic geometry in Frobenius manifolds and quantum cohomology. J. Geom. Phys. 25 (1–2) (1998), 183–204. | DOI | MR
[2] Crainic, M., Fernandes, R.L.: Lectures integrability Lie brackets. Geom. Topol. Monogr. 17 (2011), 1–107. | MR
[3] David, L., Strachan, I.A.B.: Dubrovin’s duality for F-manifolds with eventual identities. Adv. Math. 226 (4) (2011), 4031–4060. | DOI | MR
[4] Dotsenko, V.: Algebraic structures of F-manifolds via pre-Lie algebras. Ann. Mat. Pura Appl. (4) 198 (2019), 517–527. | DOI | MR
[5] Dubrovin, B.: Geometry of 2D topological field theories. Lecture Notes in Math., vol. 1620, Springer, 1996. | MR | Zbl
[6] Dubrovin, B.: On almost duality for Frobenius manifolds. Amer. Math. Soc. Transl. 212 (2004), 75–132. | MR
[7] Dubrovin, B.: WDVV Equations and Frobenius Manifolds. Encyclopedia of Mathematical Physics, vol. 1, Elsevier, 2006, pp. 438–447.
[8] Dufour, J.P., Zung, N.T.: Poisson Structures and Their Normal Forms. Birkhauser, 2000. | MR
[9] Fernandes, R.L.: Lie algebroids, holonomy and characteristic classes. Adv. Math. 170 (1) (2002), 119–179. | DOI | MR
[10] Hertling, C.: Frobenius manifolds and moduli spaces for singularities. Cambridge University Press, 2004. | MR
[11] Hertling, C., Manin, Y.: Weak Frobenius manifolds. Internat. Math. Res. Notices 6 (1999), 277–286. | DOI | MR | Zbl
[12] Hitchin, N.: Frobenius manifolds. Gauge Theory and Symplectic Geometry, Springer, 1997. | MR
[13] Kodaira, K.: Complex Manifolds and Deformation of Complex Structures. Springer, 2005. | MR
[14] Mackenzie, K.C.H.: General Theory of Lie Groupoids and Lie Algebroids. Cambridge University Press, 2005. | MR | Zbl
[15] Manetti, M.: Lectures on deformation of complex manifolds. Rendiconti di Matematica 24 (2004), 1–183. | MR
[16] Manin, Y.: Mirrors, functoriality, and derived geometry. arXiv:1708.02849.
[17] Manin, Y.: Frobenius Manifolds, Quantum Cohomology, and Moduli Spaces. Amer. Math. Soc. Colloq. Publ. 47 (1999), xiv+303 pp. | MR | Zbl
[18] Manin, Y.: F-manifolds with flat structure and Dubrovin’s duality. Adv. Math. 198 (1) (2005), 5–26. | DOI | MR
[19] Manin, Y.: Grothendieck-Verdier duality patterns in quantum algebra. Izv. Ross. Akad. Nauk Ser. Mat. 81 (4) (2017), 158–166. | MR
[20] Weinstein, A.: Linearization problems Lie algebroids and Lie groupoids. Lett. Math. Phys. 52 (2000), 93–102. | DOI | MR
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