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Partial derivatives and endomorphisms of some relatively free Lie algebras

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References

  1. J. S. Birman, “An inverse function theorem for free groups,” Proc. Amer. Math. Soc.,41, 634–638 (1973).

    Google Scholar 

  2. A. H. Schofield, Representation of Rings over Skew Fields (London Math. Soc. Lecture Note Ser.; No. 92), Cambridge Univ., Cambridge (1985).

    Google Scholar 

  3. A. V. Yagzhev, “On endomorphisms of free algebras,” Sibirsk. Mat. Zh.,21, No. 1, 181–192 (1980).

    Google Scholar 

  4. U. U. Umirbaev, “On the Jacobian of a Lie algebra,” in: Abstracts: VI Siberian School on the Varieties of Algebraic Systems (Magnitogorsk, 1990) [in Russian], Magnitogorsk, 1990, p. 32.

  5. C. Reutenauer, “Applications of a noncommutative Jacobian matrix,” J. Pure Appl. Algebra,77, No. 2, 169–181 (1992).

    Google Scholar 

  6. A. F. Krasnikov, “Generators of the groupF/[N, N],” Mat. Zametki,24, No. 2, 167–174 (1978).

    Google Scholar 

  7. V. A. Roman'kov, “A criterion of primitiveness for a system of elements in a free metabelian group,” Ukrain. Mat. Zh.,43, No. 7, 996–1002 (1991).

    Google Scholar 

  8. E. I. Timoshenko, “On inclusion of given elements in a basis for a free metabelian group,” submitted to VINITI on April 11, 1988, No. 2699.

  9. A. V. Yagzhev, “The algorithmic problem of recognizing automorphisms among the endomorphisms of free associative algebras of finite rank,” Sibirsk. Mat. Zh.,21, No. 1, 193–199 (1980).

    Google Scholar 

  10. U. U. Umirbaev, “Approximation of free Lie algebras relative to inclusion,” in: Monoids, Rings, and Algebras (Uchen. Zap. Tartu Univ.,878) [in Russian], 1990, pp. 147–152.

  11. O. G. Kharlampovich, “The Lindon condition for solvable Lie algebras,” Izv. Vyssh. Uchebn. Zaved. Mat., No. 9, 50–59 (1984).

    Google Scholar 

  12. Yu. A. Bakhturin, Identities in Lie Algebras [in Russian], Nauka, Moscow (1985).

    Google Scholar 

  13. A. A. Suslin, “On the structure of the special linear group over polynomial rings,” Izv. Akad. Nauk SSSR Ser. Mat.,41, No. 2, 235–252 (1977).

    Google Scholar 

  14. V. A. Artamonov, “Projective metabelian groups and Lie algebras,” Izv. Akad. Nauk SSSR Ser. Mat.,42, No. 2, 226–236 (1978).

    Google Scholar 

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Authors
  1. U. U. Umirbaev
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Alma-Ata. Translated fromSibirskiî Matematicheskiî Zhurnal, Vol. 34, No. 6, pp. 179–188, November–December, 1993.

Translated by A. Z. Anan'in

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Umirbaev, U.U. Partial derivatives and endomorphisms of some relatively free Lie algebras. Sib Math J 34, 1161–1170 (1993). https://doi.org/10.1007/BF00973481

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