Symmetric Zinbiel superalgebras

References

• Adashev, J., Camacho, L., Gomez-Vidal, S., Karimjanov, I. (2014). Naturally graded Zinbiel algebras with nilindex n−3. Linear Algebra Appl. 443:86–104. DOI: 10.1016/j.laa.2013.11.021.
   Web of Science ®Google Scholar
• Aguiar, M. (2000). Pre-Poisson algebras. Lett. Math. Phys. 54(4):263–277. DOI: 10.1023/A:1010818119040.
   Web of Science ®Google Scholar
• Albuquerque, H., Benayadi, S. (2004). Quadratic Malcev superalgebras. J. Pure Appl. Algebra 187(1-3):19–45. DOI: 10.1016/S0022-4049(03)00145-2.
   Web of Science ®Google Scholar
• Alvarez, M., Castilho de Mello, T., Kaygorodov, I. (2021). Central extensions of 3-dimensional Zinbiel algebras. Ric. Mat. DOI: 10.1007/s11587-021-00604-1.
   Google Scholar
• Alvarez, M., Fehlberg Júnior, R., Kaygorodov, I. (2022). The algebraic and geometric classification of Zinbiel algebras. J. Pure Appl. Algebra 226(11):107106. DOI: 10.1016/j.jpaa.2022.107106.
   Web of Science ®Google Scholar
• Benayadi, S., Mhamdi, F., Omri, S. (2021). Quadratic (resp. symmetric) Leibniz superalgebras. Commun. Algebra 49(4):1725–1750. DOI: 10.1080/00927872.2020.1850751.
   Web of Science ®Google Scholar
• Bremner, M., Dotsenko, V. (2017). Classification of regular parametrized one-relation operads. Can. J. Math. 69(5):992–1035. DOI: 10.4153/CJM-2017-018-3.
   Web of Science ®Google Scholar
• Calderón, A., Fernández Ouaridi, A., Kaygorodov, I. (2020). On the classification of bilinear maps with radical of a fixed codimension. Linear Multilinear Algebra DOI: 10.1080/03081087.2020.1849001.
   Web of Science ®Google Scholar
• Camacho, L., Cañete, E., Gómez-Vidal, S., Omirov, B. (2013). p-filiform Zinbiel algebras. Linear Algebra Appl. 438(7):2958–2972. DOI: 10.1016/j.laa.2012.11.030.
   Web of Science ®Google Scholar
• Chapoton, F. (2022). Zinbiel algebras and multiple zeta values. Doc. Math. 27:519–533. DOI: 10.25537/dm.2022v27.519-533.
   Web of Science ®Google Scholar
• Colmenarejo, L., Diehl, J., Sorea, M. (2022). A quadratic identity in the shuffle algebra and an alternative proof for de Bruijn’s formula. European J. Combin. 99:103406. DOI: 10.1016/j.ejc.2021.103406.
   Web of Science ®Google Scholar
• Covez, S., Farinati, M., Lebed, V., Manchon, D. (2019). Bialgebraic approach to rack cohomology. arXiv:1905.02754
   Google Scholar
• Diehl, J., Ebrahimi-Fard, K., Tapia, N. (2020). Time warping invariants of multidimensional time series. Acta Appl Math. 170(1):265–290. DOI: 10.1007/s10440-020-00333-x.
   Web of Science ®Google Scholar
• Diehl, J., Lyons, T., Preis, R., Reizenstein, J. (2020). Areas of areas generate the shuffle algebra. arXiv:2002.02338
   Google Scholar
• Dokas, I. (2010). Zinbiel algebras and commutative algebras with divided powers. Glasgow Math. J. 52(2):303–313. DOI: 10.1017/S0017089509990358.
   Web of Science ®Google Scholar
• Dzhumadildaev, A. (2007). Zinbiel algebras over a q-commutators. J. Math. Sci. (N.Y.). 144(2):3909–3925. DOI: 10.1007/s10958-007-0244-9.
   Google Scholar
• Dzhumadil’Daev, A. S., Tulenbaev, K. M. (2005). Nilpotency of Zinbiel algebras. J. Dyn. Control Syst. 11(2):195–213. DOI: 10.1007/s10883-005-4170-1.
   Web of Science ®Google Scholar
• Dzhumadil'Daev, A. S., Ismailov, N. A., Mashurov, F. A. (2019). On the speciality of Tortkara algebras. J. Algebra 540:1–19. DOI: 10.1016/j.jalgebra.2019.08.010.
   Web of Science ®Google Scholar
• Gainov, A. (1957). Identical relations for binary Lie rings. (Russian) Uspehi Mat. Nauk (N.S.). 12(3):141–146.
   Google Scholar
• Gainov, A. (2010). An independent system of identities for a variety of mono-Leibniz algebras. Algebra Logic. 49(2):115–119. DOI: 10.1007/s10469-010-9083-8.
   Web of Science ®Google Scholar
• Gao, X., Guo, L., Zhang, Y. (2021). Commutative matching Rota-Baxter operators, shuffle products with decorations and matching Zinbiel algebras. J. Algebra 586:402–432. DOI: 10.1016/j.jalgebra.2021.06.032.
   Web of Science ®Google Scholar
• Ikonicoff, S., Pacaud Lemay, J.-S. (2021). Cartesian differential comonads and new models of cartesian differential categories. arXiv:2108.04304
   Google Scholar
• Ismailov, N., Dzhumadil’daev, A. (2021). Binary Leibniz algebras. Math Notes. 110(3-4):322–328. DOI: 10.4213/mzm13051.
   Web of Science ®Google Scholar
• Ismailov, N., Mashurov, F., Smadyarov, N. (2022). Defining Identities for mono and binary Zinbiel algebras. J. Algebra Appl. DOI: 10.1142/S0219498823501657.
   Web of Science ®Google Scholar
• Kaygorodov, I., Lopes, S., Páez-Guillán, P. (2020). Non-associative central extensions of null-filiform associative algebras. J. Algebra 560:1190–1210. DOI: 10.1016/j.jalgebra.2020.06.013.
   Web of Science ®Google Scholar
• Kaygorodov, I., Popov, Y., Pozhidaev, A., Volkov, Y. (2018). Degenerations of Zinbiel and nilpotent Leibniz algebras. Linear Multilinear Algebra 66(4):704–716. DOI: 10.1080/03081087.2017.1319457.
   Web of Science ®Google Scholar
• Kawski, M. (2001). Chronological algebras: combinatorics and control. J. Math. Sci. (N.Y.). 103(6):725–744. DOI: 10.1023/A:1009502501461.
   Google Scholar
• Kolesnikov, P. (2016). Commutator algebras of pre-commutative algebras. Mat. Zhur. 16(2):56–70.
   Google Scholar
• Loday, J.-L. (1995). Cup-product for Leibniz cohomology and dual Leibniz algebras. Math. Scand. 77(2):189–196. DOI: 10.7146/math.scand.a-12560.
   Web of Science ®Google Scholar
• Loday, J.-L. (2007). On the algebra of quasi-shuffles. Manuscr. Math. 123(1):79–93. DOI: 10.1007/s00229-007-0086-2.
   Web of Science ®Google Scholar
• Mukherjee, G., Saha, R. (2019). Cup-product for equivariant Leibniz cohomology and Zinbiel algebras. Algebra Colloq. 26(02):271–284. DOI: 10.1142/S100538671900021X.
   Web of Science ®Google Scholar
• Naurazbekova, A. (2019). On the structure of free dual Leibniz algebras. EMJ. 10(3):40–47. DOI: 10.32523/2077-9879-2019-10-3-40-47.
   Web of Science ®Google Scholar
• Naurazbekova, A., Umirbaev, U. (2010). Identities of dual Leibniz algebras. TWMS J. Pure Appl. Math. 1(1):86–91.
   Google Scholar
• Towers, D. (2022). Zinbiel algebras are nilpotent. J. Algebra Appl. DOI: 10.1142/S0219498823501669.
   Web of Science ®Google Scholar