The 𝓞N-structure on bimodules over associative conformal algebras

References

• Baxter, G. (1960). An analytic problem whose solution follows from a simple algebraic identity. Pacific J. Math. 10:731–742. DOI: 10.2140/pjm.1960.10.731.
   Google Scholar
• Bakalov, B., D’Andrea, A., Kac, V. G. (2001). Theory of finite pseudoalgebras. Adv. Math. 162:1–140. DOI: 10.1006/aima.2001.1993.
   Web of Science ®Google Scholar
• Bakalov, B., Kac, V. G., Voronov, A. (1999). Cohomology of conformal algebras. Comm. Math. Phys. 200(3): 561–589. DOI: 10.1007/s002200050541.
   Web of Science ®Google Scholar
• Belavin, A. A., Polyakov, A. M., Zamolodchikov, A. B. (1984). Infinite conformal symmetry in two-dimensional quantum field theory. Nuclear Phys. 241(2):333–380. DOI: 10.1016/0550-3213(84)90052-X.
   Web of Science ®Google Scholar
• Bokut, L. A., Fong, Y., Ke, W. F. (1997). Free associative conformal algebras. Proceedings of the 2nd Tainan-Moscow Algebra and Combinatorics Workshop, Tainan, pp. 13–25.
   Google Scholar
• Bokut, L. A., Fong, Y., Ke, W. F. (2000). Grobner-Shirshov bases and composition lemma for associative conformal algebras: an example. Contemp. Math. 264: 63–90.
   Google Scholar
• Bokut, L. A., Fong, Y., Ke, W. F. (2004). Composition-Diamond lemma for associative conformal algebras. J. Algebra 272(2):739–774. DOI: 10.1016/S0021-8693(03)00341-7.
   Web of Science ®Google Scholar
• Boyallian, C., Kac, V. G, Liberati, J. (2003). On the classification of subalgebras of CendN and gcN. J. Algebra 260(1):32–63. DOI: 10.1016/S0021-8693(02)00632-4.
   Google Scholar
• Cheng, S., Kac, V. G. (1997). Conformal modules. Asian J. Math. 1(1):181–193. DOI: 10.4310/AJM.1997.v1.n1.a6.
   Google Scholar
• Cheng, S., Kac, V. G., Wakimoto, M. (1998). Extensions of conformal modules. In: Kashiwara, M., Matsuo, A., Saito, K., Satake, I., eds. Topological Field Theory, Primitive Forms and Related Topics (Kyoto). Progress in Mathematics, Vol. 160. Boston: Birkhauser, pp: 33–57.
   Google Scholar
• D’Andrea, A., Kac, V. G. (1998). Structure theory of finite conformal algebras. Sel. Math. New Ser. 4(3):377–418. DOI: 10.1007/s000290050036.
   Google Scholar
• Das, A. (2020). Deformations of associative Rota-Baxter operators. J. Algebra 560:144–180. DOI: 10.1016/j.jalgebra.2020.05.016.
   Web of Science ®Google Scholar
• Guo, L. (2012). An Introduction to Rota-Baxter Algebra. Surveys of Modern Mathematics, 4. Somerville, MA: International Press; Beijing: Higher Education Press.
   Google Scholar
• Hong, Y. (2019). Extending structures for associative conformal algebras. Linear Multilinear Algebra 67(1): 196–212. DOI: 10.1080/03081087.2017.1416056.
   Web of Science ®Google Scholar
• Hong, Y., Bai, C. (2020). Conformal classical Yang-Baxter equation, S-equation and O-operators. Lett. Math. Phys. 110(5):885–909. DOI: 10.1007/s11005-019-01243-2.
   Google Scholar
• Hong, Y., Bai, C. (2021). On antisymmetric infinitesimal conformal bialgebra. J. Algebra 586:325–356. DOI: 10.1016/j.jalgebra.2021.06.029.
   Web of Science ®Google Scholar
• Kac, V. G. (1998). Vertex Algebras for Beginners, 2nd ed. Providence, RI: American Mathematical Society.
   Google Scholar
• Kac, V. G. (1999). Formal distribution algebras and conformal algebras. In: XIIth International Congress of Mathematical Physics, Cambridge: International Press, pp. 80–97.
   Google Scholar
• Kolesnikov, P. S. (2006). Simple associative conformal algebras of linear growth. J. Algebra 295(1):247–268. DOI: 10.1016/j.jalgebra.2005.08.004.
   Web of Science ®Google Scholar
• Kolesnikov, P. S. (2006). Associative conformal algebras with finite faithful representation. Adv. Math. 202(2): 602–637. DOI: 10.1016/j.aim.2005.04.001.
   Web of Science ®Google Scholar
• Kolesnikov, P. S. (2007). On the Wedderburn principal theorem in conformal algebras. J. Algebra Appl. 6(1): 119–134. DOI: 10.1142/S0219498807002120.
   Web of Science ®Google Scholar
• Kolesnikov, P. S. (2011). On finite representations of conformal algebras. J. Algebra 331(1):169–193. DOI: 10.1016/j.jalgebra.2010.12.014.
   Web of Science ®Google Scholar
• Kolesnikov, P. S., Kozlov, R. A. (2019). On the Hochschild cohomologies of associative conformal algebras with a finite faithful representation. Commun. Math. Phys. 369(1):351–370. DOI: 10.1007/s00220-019-03309-7.
   Web of Science ®Google Scholar
• Lazarev, A., Sheng, Y., Tang, R. (2021). Deformations and homotopy theory of relative Rota-Baxter Lie algebras. Commun. Math. Phys. 383(1):595–631. DOI: 10.1007/s00220-020-03881-3.
   Web of Science ®Google Scholar
• Liu, J., Bai, C., Sheng, Y. (2019). Compatible O-operators on bimodules over associative algebras. J. Algebra 532: 80–118. DOI: 10.1016/j.jalgebra.2019.05.013.
   Web of Science ®Google Scholar
• Magri F., Morosi C. (1984). A geometrical characterization of integrable Hamiltonian systems through the theory of Poisson-Nijenhuis manifolds. In: Quaderno S19, University of Milan.
   Google Scholar
• Ravanpak Z., Rezaei-Aghdam A., Haghighatdoost G. (2018). Invariant Poisson-Nijenhuis structures on Lie groups and classification. Int. J. Geom. Methods Mod. Phys. 15:1850059.
   Web of Science ®Google Scholar
• Retakh, A. (2001). Associative conformal algebras of linear growth. J. Algebra 237(2):769–788. DOI: 10.1006/jabr.2000.8616.
   Web of Science ®Google Scholar
• Retakh, A. (2006). On associative conformal algebras of linear growth II. J. Algebra 304(1):543–556. DOI: 10.1016/j.jalgebra.2005.11.004.
   Web of Science ®Google Scholar
• Roitman, M. (2000). Universal enveloping conformal algebras. Sel. Math. New Ser. 6(3):319–345. DOI: 10.1007/PL00001391.
   Google Scholar
• Roitman, M. (2005). On embedding of Lie conformal algebras into associative conformal algebras. J. Lie theory 15(2):575–588.
   Web of Science ®Google Scholar
• Rota, G. C. (1969). Baxter algebras and combinatorial identities I, II. Bull. Am. Math. Soc. 75:325–329, 330–334. DOI: 10.1090/S0002-9904-1969-12156-7.
   Web of Science ®Google Scholar
• Tang, R., Bai, C., Guo, L., Sheng, Y. (2019). Deformations and their controlling cohomologies of O-operators. Commun. Math. Phys. 368(2):665–700. DOI: 10.1007/s00220-019-03286-x.
   Web of Science ®Google Scholar
• Tang, R., Sheng, Y., Zhou, Y. (2020). Deformations of relative Rota-Baxter operators on Leibniz algebras. Int. J. Geom. Methods Mod. Phys. 17(12): 2050174. DOI: 10.1142/S0219887820501741.
   Web of Science ®Google Scholar
• Tang, R., Hou, S., Sheng, Y. (2021). Lie 3-algebras and deformations of relative Rota-Baxter operators on 3-Lie algebras. J. Algebra 567:37–62. DOI: 10.1016/j.jalgebra.2020.09.017.
   Web of Science ®Google Scholar
• Uchino, K. (2008). Quantum analogy of Poisson geometry, related dendriform algebras and Rota-Baxter operators. Lett. Math. Phys. 85(2–3):91–109. DOI: 10.1007/s11005-008-0259-2.
   Web of Science ®Google Scholar
• Uchino, K. (2010). Twisting on associative algebras and Rota-Baxter type operators. J. Noncommut. Geom. 4(3):349–379. DOI: 10.4171/JNCG/59.
   Web of Science ®Google Scholar
• Uchino, K. (2010). Derived bracket construction and Manin products. Lett. Math. Phys. 93(1):37–53. DOI: 10.1007/s11005-010-0400-x.
   Web of Science ®Google Scholar
• Voronov, Th. (2005). Higher derived brackets and homotopy algebras. J. Pure Appl. Algebra 202(1–3):133–153. DOI: 10.1016/j.jpaa.2005.01.010.
   Web of Science ®Google Scholar
• Wang, K., Zhou, G. (2021). Deformations and homotopy theory of Ropta-Baxter algebra of any weight. arXiv: 2108.06744.
   Google Scholar
• Yuan L. (2022). O-operators and Nijenhius operators of associative conformal algebras. J. Algebra 609:245–291. DOI: 10.1016/j.jalgebra.2022.07.003.
   Google Scholar