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Funktsional. Anal. i Prilozhen., 2005, Volume 39, Issue 3, Pages 14–27 (Mi faa71)  

This article is cited in 3 scientific papers (total in 3 papers)

Algebras Generated by Linearly Dependent Elements with Prescribed Spectra

M. A. Vlasenko, A. S. Mellit, Yu. S. Samoilenko

Institute of Mathematics, Ukrainian National Academy of Sciences

Abstract: We consider associative algebras presented by a finite set of generators and relations of special form: each generator is annihilated by some polynomial, and the sum of generators is zero. The growth of this algebra in dependence on the degrees of the polynomials annihilating the generators is studied. The tuples of degrees for which the algebras are finite-dimensional, have polynomial growth, or have exponential growth are indicated. To the tuple of degrees, we assign a graph, and the above-mentioned cases correspond to Dynkin diagrams, extended Dynkin diagrams, and the other graphs, respectively. For extended Dynkin diagrams, we indicate the hyperplane in the space of parameters (roots of the polynomials) on which the corresponding algebras satisfy polynomial identities.

Keywords: PI algebra, finitely generated algebra, Dynkin diagram, polynomial growth, deformed preprojective algebra

DOI: https://doi.org/10.4213/faa71

Full text: PDF file (246 kB)
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English version:
Functional Analysis and Its Applications, 2005, 39:3, 175–186

Bibliographic databases:

UDC: 517.95
Received: 10.09.2003

Citation: M. A. Vlasenko, A. S. Mellit, Yu. S. Samoilenko, “Algebras Generated by Linearly Dependent Elements with Prescribed Spectra”, Funktsional. Anal. i Prilozhen., 39:3 (2005), 14–27; Funct. Anal. Appl., 39:3 (2005), 175–186

Citation in format AMSBIB
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\paper Algebras Generated by Linearly Dependent Elements with Prescribed Spectra
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\issue 3
\pages 14--27
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\pages 175--186
\crossref{https://doi.org/10.1007/s10688-005-0036-2}
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    This publication is cited in the following articles:
    1. I. K. Redchuk, “Separating functions and their applications”, J. Math. Sci. (N. Y.), 145:1 (2007), 4805–4810  mathnet  crossref  mathscinet  zmath  elib
    2. Albeverio S., Ostrovskyi V., Samoilenko Yu., “On functions on graphs and representations of a certain class of *-algebras”, J. Algebra, 308:2 (2007), 567–582  crossref  mathscinet  zmath  isi  scopus
    3. Rabanovych V.I., “on Decompositions of a Scalar Operator Into a Sum of Self-Adjoint Operators With Finite Spectrum”, Ukr. Math. J., 67:5 (2015), 795–813  crossref  mathscinet  zmath  isi  scopus
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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