Abstract
We show that a space of one variable differential operators of order p admits non-trivial 2p-commutator and the number 2p here can not be improved.
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Amitsur, A.S., Levitzki, J.: Minimal identities for algebras. Proc. AMS 1(1050), 449–463
Dzhumadil’daev A.S.: Minimal identities for right-symmetric algebras. J. Algebra 225, 201–230 (2000)
Dzhumadil’daev A.S.: N-commutators. Comm. Math. Helv. 79(3), 516–553 (2004)
Dzhumadil’daev, A.S.: n-Lie structures that are generated by wronskians. Sibirskii Matematicheskii Zhurnal 46(4), 759–773 (2005). [2005 =engl. transl. Siberian Mathematical Journal 46(4), 601–612 (2005)]
Hanlon P., Wachs M.: On Lie k-algebras. Adv. Math. 113, 206–236 (1995)
Kirillov A.A., Kontsevich M.L., Molev A.I.: Algebras of intermediate growth. Sel. Math. Sov. 9(2), 138–153 (1990)
Martindale W.S.: III Prime rings satisfying a generalized polynomial identity. J. Algebra 12, 576–584 (1969)
Molev, A.I.: A proof of the Kirillov–Kontsevich formula. Russ. Math. Surv. 391, 171–172 (1984)
Razmyslov, Y.P.:Identities of algebras and their representations. In: English Translations in Translations of Mathematical Monographs (1989), vol. 138, pp. xiii, 318. American Mathematical Society (AMS), Providence, RI (1994)
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Dzhumadil’daev, A. 2p-Commutator on Differential Operators of Order p . Lett Math Phys 104, 849–869 (2014). https://doi.org/10.1007/s11005-014-0695-0
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DOI: https://doi.org/10.1007/s11005-014-0695-0