Classification of naturally graded nilpotent associative algebras

References

• Adashev, J. K., Ladra, M., Omirov, B. A. (2019). Classification of naturally graded Zinbiel algebras with characteristic sequence equal to (n−p,p). Ukr. Math. J. 71(7):985–1005. DOI: 10.1007/s11253-019-01693-w.
   Google Scholar
• Cartan, E. (1898). Les groupes bilinéaires et les systèmes de nombres complexes. Ann. Fac. Sci. Toulouse Sci. Math. Sci. Phys. 12(2):B65–B99. DOI: 10.5802/afst.143.
   Google Scholar
• De Graaf, W. A. (2018). Classification of nilpotent associative algebras of small dimension. Int. J. Algebra Comput. 28(1):133–161. DOI: 10.1142/S0218196718500078.
   Web of Science ®Google Scholar
• Eick, B., Moede, T. (2015). Nilpotent associative algebras and coclass theory. J. Algebra 434:249–260. DOI: 10.1016/j.jalgebra.2015.03.027.
   Web of Science ®Google Scholar
• Eick, B., Moede, T. (2017). Coclass theory for finite nilpotent associative algebras: algorithms and a periodicity conjecture. Exp. Math. 26(3):267–274. DOI: 10.1080/10586458.2016.1162229.
   Web of Science ®Google Scholar
• Elduque, A., Kochetov, M., Rodrigo-Escudero, A. (2022). Gradings on associative algebras with involution and real forms of classical simple Lie algebras. J. Algebra 590:61–138. DOI: 10.1016/j.jalgebra.2021.10.006.
   Google Scholar
• Frobenius, G. (1903). Theorie der hyperkomplexen Größen I. II. Sitz. Kön. Preuss. Akad. Wiss. 504–537, 634–645
   Google Scholar
• Hazlett, O. C. (1916). On the classification and invariantive characterization of nilpotent algebras. Amer. J. Math. 38(2):109–138. DOI: 10.2307/2370262.
   Google Scholar
• Karimjanov, I. A. (2021). The classification of 5-dimensional complex nilpotent associative algebras. Commun. Algebra 49(3):915–931. DOI: 10.1080/00927872.2020.1822371.
   Web of Science ®Google Scholar
• Karimjanov, I. A., Kaygorodov, I., Ladra, M. (2021). Central extensions of filiform associative algebras. Linear Multilinear Algebra 69(6):1083–1101. DOI: 10.1080/03081087.2019.1620674.
   Web of Science ®Google Scholar
• Karimjanov, I. A., Ladra, M. (2020). Some classes of nilpotent associative algebras. Mediterr. J. Math. 17:70. DOI: 10.1007/s00009-020-1504-x.
   Google Scholar
• Kaygorodov, I., Rakhimov, I., Said Husain, Sh. K. (2020). The algebraic classification of nilpotent associative commutative algebras. J. Algebra Appl. 19(11):2050220. DOI: 10.1142/S0219498820502205.
   Google Scholar
• Kruse, R. L., Price, D. T. (1969). Nilpotent rings. New York-London-Paris: Gordon and Breach Science Publishers
   Google Scholar
• Masutova, K. K., Omirov, B. A. (2014). On some zero-filiform algebras. Ukr. Math. J. 66(4):541–552. DOI: 10.1007/s11253-014-0951-6.
   Web of Science ®Google Scholar
• Masutova, K. K., Omirov, B. A., Khudoyberdiyev, A. Kh. (2013). Naturally graded Leibniz algebras with characteristic sequence (n−m,m). Math. Notes 93(5):740–755. DOI: 10.4213/mzm8894.
   Google Scholar
• Mazzolla, G. (1979). The algebraic and geometric classification of associative algebras of dimension five. Manuscr. Math. 27(1):81–101. DOI: 10.1007/BF01297739.
   Web of Science ®Google Scholar
• Mazzolla, G. (1980). Generic finite schemes and Hochschild cocycles. Comment. Math. Helv. 55(2):267–293. DOI: 10.1007/BF02566686.
   Web of Science ®Google Scholar
• Molien, T. (1892) Ueber Systeme höherer complexer Zahlen. Math. Ann. 41(1):83–156. DOI: 10.1007/BF01443450.
   Google Scholar
• Peirce, B. (1881). Linear associative algebra. Amer. J. Math. 4:97–229. DOI: 10.2307/2369153.
   Google Scholar
• Poonen, B. (2008). Isomorphism types of commutative algebras of finite rank over an algebraically closed field. In: Computational Arithmetic Geometry, Contemporary Mathematics. Providence, RI: AMS, pp. 111–120. DOI: 10.1090/conm/463/09050.
   Google Scholar
• Siles Molina, M. (2006). Finite Z-gradings of simple associative algebras. J. Pure Appl. Algebra 207(3):619–630. DOI: 10.1016/j.jpaa.2005.10.005.
   Google Scholar
• Smirnov, O. N. (1997). Simple associative algebras with finite Z-grading. J. Algebra 196(1):171–184. DOI: 10.1006/jabr.1997.7087.
   Google Scholar
• Wedderburn, J. H. M. (1908). On hypercomplex numbers. Proc. Lond. Math. Soc. (2) 6:77–118. DOI: 10.1112/plms/s2-6.1.77.
   Google Scholar