Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Codimensions of polynomial identities of representations of Lie algebras
HTML articles powered by AMS MathViewer

by A. S. Gordienko PDF
Proc. Amer. Math. Soc. 141 (2013), 3369-3382 Request permission

Abstract:

Consider a representation $\rho \colon L \to \mathfrak {gl}(V)$ where $L$ is a Lie algebra and $V$ is a finite dimensional vector space. We prove the analog of Amitsur’s conjecture on asymptotic behavior for codimensions of polynomial identities of $\rho$.
References
  • Antonio Giambruno and Mikhail Zaicev, Polynomial identities and asymptotic methods, Mathematical Surveys and Monographs, vol. 122, American Mathematical Society, Providence, RI, 2005. MR 2176105, DOI 10.1090/surv/122
  • M. V. Zaĭtsev, Integrality of exponents of growth of identities of finite-dimensional Lie algebras, Izv. Ross. Akad. Nauk Ser. Mat. 66 (2002), no. 3, 23–48 (Russian, with Russian summary); English transl., Izv. Math. 66 (2002), no. 3, 463–487. MR 1921808, DOI 10.1070/IM2002v066n03ABEH000386
  • Yu. P. Razmyslov, Identities of algebras and their representations, Translations of Mathematical Monographs, vol. 138, American Mathematical Society, Providence, RI, 1994. Translated from the 1989 Russian original by A. M. Shtern. MR 1291603, DOI 10.1090/mmono/138
  • B. I. Plotkin and S. M. Vovsi, Mnogoobraziya predstavleniĭ grupp, “Zinatne”, Riga, 1983 (Russian). Obshchaya teoriya, svyazi i prilozheniya. [General theory, connections and applications]. MR 739330
  • Morikuni Goto and Frank D. Grosshans, Semisimple Lie algebras, Lecture Notes in Pure and Applied Mathematics, Vol. 38, Marcel Dekker, Inc., New York-Basel, 1978. MR 0573070
  • Yu. A. Bahturin, Identical relations in Lie algebras, VNU Science Press, b.v., Utrecht, 1987. Translated from the Russian by Bahturin. MR 886063
  • Vesselin Drensky, Free algebras and PI-algebras, Springer-Verlag Singapore, Singapore, 2000. Graduate course in algebra. MR 1712064
  • Nathan Jacobson, Basic algebra. II, 2nd ed., W. H. Freeman and Company, New York, 1989. MR 1009787
  • James E. Humphreys, Introduction to Lie algebras and representation theory, Graduate Texts in Mathematics, vol. 9, Springer-Verlag, New York-Berlin, 1978. Second printing, revised. MR 499562
Similar Articles
Additional Information
  • A. S. Gordienko
  • Affiliation: Memorial University of Newfoundland, St. John’s, NL, Canada
  • Email: alexey.gordienko@vub.ac.be
  • Received by editor(s): June 17, 2011
  • Received by editor(s) in revised form: December 15, 2011
  • Published electronically: June 18, 2013
  • Additional Notes: This work was supported by postdoctoral fellowships from the Atlantic Association for Research in Mathematical Sciences (AARMS), the Atlantic Algebra Centre (AAC), Memorial University of Newfoundland (MUN), and the Natural Sciences and Engineering Research Council of Canada (NSERC)
  • Communicated by: Kailash C. Misra
  • © Copyright 2013 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 141 (2013), 3369-3382
  • MSC (2010): Primary 17B01; Secondary 16R10, 17B10, 20C30
  • DOI: https://doi.org/10.1090/S0002-9939-2013-11622-9
  • MathSciNet review: 3080160