Previous |  Up |  Next

Article

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
.
Category: math
.
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
.
Date available: 2022-11-28T11:43:42Z
Last updated: 2023-04-11
Stable URL: http://hdl.handle.net/10338.dmlcz/151141
.
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
.

Fulltext not available (moving wall 24 months)

Partner of
EuDML logo