Title: | On the classification of $3$-dimensional $F$-manifold algebras (English) |
Author: | Chen, Zhiqi |
Author: | Li, Jifu |
Author: | Ding, Ming |
Language: | English |
Journal: | Czechoslovak Mathematical Journal |
ISSN: | 0011-4642 (print) |
ISSN: | 1572-9141 (online) |
Volume: | 72 |
Issue: | 4 |
Year: | 2022 |
Pages: | 1191-1204 |
Summary lang: | English |
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Category: | math |
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Summary: | $F$-manifold algebras are focused on the algebraic properties of the tangent sheaf of $F$-manifolds. The local classification of 3-dimensional $F$-manifolds has been given in A. Basalaev, C. Hertling (2021). We study the classification of 3-dimensional $F$-manifold algebras over the complex field $\mathbb {C}$. (English) |
Keyword: | $F$-manifold |
Keyword: | Poisson algebra |
Keyword: | $F$-manifold algebra |
MSC: | 17A30 |
MSC: | 17B60 |
idZBL: | Zbl 07655794 |
idMR: | MR4517607 |
DOI: | 10.21136/CMJ.2022.0017-22 |
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Date available: | 2022-11-28T11:43:42Z |
Last updated: | 2023-04-11 |
Stable URL: | http://hdl.handle.net/10338.dmlcz/151141 |
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Reference: | [1] Bai, C., Meng, D.: The classification of Novikov algebras in low dimensions.J. Phys. A, Math. Gen. 34 (2001), 1581-1594. Zbl 1001.17002, MR 1818753, 10.1088/0305-4470/34/8/305 |
Reference: | [2] Basalaev, A., Hertling, C.: 3-dimensional $F$-manifolds.Lett. Math. Phys. 111 (2021), Article ID 90, 50 pages. Zbl 1471.32040, MR 4282746, 10.1007/s11005-021-01432-y |
Reference: | [3] Hassine, A. Ben, Chtioui, T., Maalaoui, M. A., Mabrouk, S.: On Hom-$F$-manifold algebras and quantization.Available at https://arxiv.org/abs/2102.05595 (2021), 23 pages. MR 4456933 |
Reference: | [4] Morales, J. A. Cruz, Gutierrez, J. A., Torres-Gomez, A.: $F$-algebra-Rinehart pairs and super $F$-algebroids.Available at https://arxiv.org/abs/1904.04724v2 (2019), 14 pages. MR 4515932 |
Reference: | [5] Chari, V., Pressley, A.: A Guide to Quantum Groups.Cambridge University Press, Cambridge (1994). Zbl 0839.17010, MR 1300632 |
Reference: | [6] Ding, M., Chen, Z., Li, J.: $F$-manifold color algebras.Available at https://arxiv.org/abs/2101.00959v2 (2021), 13 pages. |
Reference: | [7] Dotsenko, V.: Algebraic structures of $F$-manifolds via pre-Lie algebras.Ann. Mat. Pura Appl. (4) 198 (2019), 517-527. Zbl 07041963, MR 3927168, 10.1007/s10231-018-0787-z |
Reference: | [8] Dubrovin, B.: Geometry of 2D topological field theories.Integrable Systems and Quantum Groups Lecture Notes in Mathematics 1620. Springer, Berlin (1996), 120-348. Zbl 0841.58065, MR 1397274, 10.1007/BFb0094793 |
Reference: | [9] Fulton, W., Harris, J.: Representation Theory: A First Course.Graduate Texts in Mathematics 129. Springer, New York (1991). Zbl 0744.22001, MR 1153249, 10.1007/978-1-4612-0979-9 |
Reference: | [10] Hertling, C.: Frobenius Manifolds and Moduli Spaces for Singularities.Cambridge Tracts in Mathematics 151. Cambridge University Press, Cambridge (2002). Zbl 1023.14018, MR 1924259, 10.1017/CBO9780511543104 |
Reference: | [11] Hertling, C., Manin, Y.: Weak Frobenius manifolds.Int. Math. Res. Not. 1999 (1999), 277-286. Zbl 0960.58003, MR 1680372, 10.1155/S1073792899000148 |
Reference: | [12] Liu, J., Bai, C., Sheng, Y.: Noncommutative Poisson bialgebras.J. Algebra 556 (2020), 35-66. Zbl 1475.17038, MR 4082054, 10.1016/j.jalgebra.2020.03.009 |
Reference: | [13] Liu, J., Sheng, Y., Bai, C.: $F$-manifold algebras and deformation quantization via pre-Lie algebras.J. Algebra 559 (2020), 467-495. Zbl 1442.17003, MR 4097911, 10.1016/j.jalgebra.2020.04.029 |
Reference: | [14] Ni, X., Bai, C.: Poisson bialgebras.J. Math. Phys. 54 (2013), Article ID 023515, 14 pages. Zbl 1290.17019, MR 3076642, 10.1063/1.4792668 |
Reference: | [15] Patera, J., Sharp, R. T., Winternitz, P., Zassenhaus, H.: Invariants of real low dimension Lie algebras.J. Math. Phys. 17 (1976), 986-994. Zbl 0357.17004, MR 0404362, 10.1063/1.522992 |
Reference: | [16] Šnobl, L., Winternitz, P.: Classification and Identification of Lie Algebras.CRM Monograph Series 33. AMS, Providence (2014). Zbl 1331.17001, MR 3184730, 10.1090/crmm/033 |
Reference: | [17] Uchino, K.: Quantum analogy of Poisson geometry, related dendriform algebras and Rota-Baxter operators.Lett. Math. Phys. 85 (2008), 91-109. Zbl 1243.17002, MR 2443932, 10.1007/s11005-008-0259-2 |
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