General information
Latest issue
Forthcoming papers
Impact factor
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

Latest issue
Current issues
Archive issues
What is RSS

Izv. RAN. Ser. Mat.:

Personal entry:
Save password
Forgotten password?

Izv. Akad. Nauk SSSR Ser. Mat., 1981, Volume 45, Issue 1, Pages 143–166 (Mi izv1551)  

This article is cited in 15 scientific papers (total in 15 papers)

Algebras satisfying Capelli identities

Yu. P. Razmyslov

Abstract: In this paper the author considers the representation of an algebra $L$ of a certain signature in an algebra $A$ (generally of a different signature) satisfying identity relations of Capelli type. A criterion for the Capelli identities to hold in the pair $(A,L)$ is indicated, and a structural description of such pairs is given. The results are applied for the case where $L$ is a Lie algebra and $A$ is its associative enveloping algebra. In addition, from these results it is deduced that an “algebraicity” identity over a field of characteristic zero implies nilpotence of the Jacobson radical of a finitely generated associative algebra.
Bibliography: 10 titles.

Full text: PDF file (2657 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Izvestiya, 1982, 18:1, 125–144

Bibliographic databases:

UDC: 519.4
MSC: Primary 16A38, 17A30; Secondary 17B05, 17C05
Received: 12.02.1980

Citation: Yu. P. Razmyslov, “Algebras satisfying Capelli identities”, Izv. Akad. Nauk SSSR Ser. Mat., 45:1 (1981), 143–166; Math. USSR-Izv., 18:1 (1982), 125–144

Citation in format AMSBIB
\by Yu.~P.~Razmyslov
\paper Algebras satisfying Capelli identities
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1981
\vol 45
\issue 1
\pages 143--166
\jour Math. USSR-Izv.
\yr 1982
\vol 18
\issue 1
\pages 125--144

Linking options:

    SHARE: FaceBook Twitter Livejournal

    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Yu. P. Razmyslov, “Central polynomials in irreducible representations of a semisimple Lie algebra”, Math. USSR-Sb., 50:1 (1985), 99–124  mathnet  crossref  mathscinet  zmath
    2. A. R. Kemer, “Varieties and $Z_2$-graded algebras”, Math. USSR-Izv., 25:2 (1985), 359–374  mathnet  crossref  mathscinet  zmath
    3. M. V. Zaicev, “Special Lie algebras”, Russian Math. Surveys, 48:6 (1993), 111–152  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. Yu. P. Razmyslov, K. A. Zubrilin, “On the nilpotency of obstructions for the representability of algebras satisfying Capelli identities and representations of finite type”, Russian Math. Surveys, 48:6 (1993), 183–184  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    5. K. A. Zubrilin, “Algebras satisfying Capelli identities”, Sb. Math., 186:3 (1995), 359–370  mathnet  crossref  mathscinet  zmath  isi
    6. K. A. Zubrilin, “O klasse nilpotentnosti prepyatstviya dlya predstavimosti algebr, udovletvoryayuschikh tozhdestvam Kapelli”, Fundament. i prikl. matem., 1:2 (1995), 409–430  mathnet  mathscinet  zmath
    7. K. A. Zubrilin, “On the largest nilpotent ideal in algebras satisfying Capelli identities”, Sb. Math., 188:8 (1997), 1203–1211  mathnet  crossref  crossref  mathscinet  zmath  isi
    8. K. A. Zubrilin, “On the Baer ideal in algebras satisfying Capelli identities”, Sb. Math., 189:12 (1998), 1809–1818  mathnet  crossref  crossref  mathscinet  zmath  isi
    9. A. Ya. Belov, “The Gel'fand–Kirillov dimension of relatively free prime algebras of arbitrary signature”, Russian Math. Surveys, 58:4 (2003), 777–779  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    10. A. Ya. Belov, “No associative $PI$-algebra coincides with its commutant”, Siberian Math. J., 44:6 (2003), 969–980  mathnet  crossref  mathscinet  zmath  isi  elib
    11. A. Ya. Belov, “The Kurosh problem, height theorem, nilpotency of the radical, and algebraicity identity”, J. Math. Sci., 154:2 (2008), 125–142  mathnet  crossref  mathscinet  zmath  elib  elib
    12. A. Ya. Belov, “Burnside-type problems, theorems on height, and independence”, J. Math. Sci., 156:2 (2009), 219–260  mathnet  crossref  mathscinet  zmath  elib  elib
    13. A. Ya. Belov, “On Rings Asymptotically Close to Associative Rings”, Siberian Adv. Math., 17:4 (2007), 227–267  mathnet  crossref  mathscinet  elib
    14. A. Ya. Belov, “The local finite basis property and local representability of varieties of associative rings”, Izv. Math., 74:1 (2010), 1–126  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    15. Belov-Kanel A., Giambruno A., Rowen L.H., Vishne U., “Zariski Closed Algebras in Varieties of Universal Algebra”, Algebr. Represent. Theory, 17:6 (2014), 1771–1783  crossref  isi
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
    Number of views:
    This page:269
    Full text:104
    First page:1

    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2021