Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Polynomial growth of the codimensions: a characterization


Authors: A. Giambruno and S. Mishchenko
Journal: Proc. Amer. Math. Soc. 138 (2010), 853-859
MSC (2010): Primary 17A50, 16R10, 16P90; Secondary 20C30
DOI: https://doi.org/10.1090/S0002-9939-09-10160-0
Published electronically: November 10, 2009
MathSciNet review: 2566551
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ A$ be a not necessarily associative algebra over a field of characteristic zero. Here we characterize the T-ideal of identities of $ A$ in case the corresponding sequence of codimensions is polynomially bounded.


References [Enhancements On Off] (What's this?)

  • 1. I. I. Benediktovič and A. E. Zalesskiĭ, 𝑇-ideals of free Lie algebras with polynomial growth of a sequence of codimensionalities, Vestsī Akad. Navuk BSSR Ser. Fīz.-Mat. Navuk 3 (1980), 5–10, 139 (Russian, with English summary). MR 582766
  • 2. Vesselin Drensky, Free algebras and PI-algebras, Springer-Verlag Singapore, Singapore, 2000. Graduate course in algebra. MR 1712064
  • 3. Antonio Giambruno and Mikhail Zaicev, Polynomial identities and asymptotic methods, Mathematical Surveys and Monographs, vol. 122, American Mathematical Society, Providence, RI, 2005. MR 2176105
  • 4. Gordon James and Adalbert Kerber, The representation theory of the symmetric group, Encyclopedia of Mathematics and its Applications, vol. 16, Addison-Wesley Publishing Co., Reading, Mass., 1981. With a foreword by P. M. Cohn; With an introduction by Gilbert de B. Robinson. MR 644144
  • 5. A. R. Kemer, The Spechtian nature of 𝑇-ideals whose condimensions have power growth, Sibirsk. Mat. Ž. 19 (1978), no. 1, 54–69, 237 (Russian). MR 0466190
  • 6. S. P. Mishchenko, Lower bounds on the dimensions of irreducible representations of symmetric groups and of the exponents of the exponential of varieties of Lie algebras, Mat. Sb. 187 (1996), no. 1, 83–94 (Russian, with Russian summary); English transl., Sb. Math. 187 (1996), no. 1, 81–92. MR 1380205, https://doi.org/10.1070/SM1996v187n01ABEH000101
  • 7. S. Mishchenko, Varieties with colength equal to one (Russian), Vest. Mosk. Univ., Ser. I-Mat. (to appear).
  • 8. Amitai Regev, Existence of identities in 𝐴⊗𝐵, Israel J. Math. 11 (1972), 131–152. MR 0314893, https://doi.org/10.1007/BF02762615
  • 9. I. B. Volichenko, Varieties of Lie algebras with identity [[𝑋₁,𝑋₂,𝑋₃],[𝑋₄,𝑋₅,𝑋₆]]=0 over a field of characteristic zero, Sibirsk. Mat. Zh. 25 (1984), no. 3, 40–54 (Russian). MR 746940
  • 10. K. A. Zhevlakov, A. M. Slin′ko, I. P. Shestakov, and A. I. Shirshov, Rings that are nearly associative, Pure and Applied Mathematics, vol. 104, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1982. Translated from the Russian by Harry F. Smith. MR 668355

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 17A50, 16R10, 16P90, 20C30

Retrieve articles in all journals with MSC (2010): 17A50, 16R10, 16P90, 20C30


Additional Information

A. Giambruno
Affiliation: Dipartimento di Matematica e Applicazioni, Università di Palermo, Via Archirafi 34, 90123 Palermo, Italy
Email: a.giambruno@unipa.it

S. Mishchenko
Affiliation: Department of Algebra and Geometric Computations, Ulyanovsk State University, Ulyanovsk 432970, Russia
Email: mishchenkosp@mail.ru

DOI: https://doi.org/10.1090/S0002-9939-09-10160-0
Keywords: Polynomial identity, cocharacter, codimension
Received by editor(s): March 9, 2009
Received by editor(s) in revised form: August 6, 2009
Published electronically: November 10, 2009
Additional Notes: The first author was partially supported by MIUR of Italy
The second author was partially supported by RFBR grant 07-01-00080.
Communicated by: Martin Lorenz
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.