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Mat. Sb., 2000, Volume 191, Number 4, Pages 67–90 (Mi msb471)  

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

Balanced systems of primitive idempotents in matrix algebras

D. N. Ivanov

M. V. Lomonosov Moscow State University

Abstract: The article develops the concept of balanced $t$-systems of idempotents in associative semisimple finite-dimensional algebras over the field of complex numbers $\mathbb C$ this was introduced by the author as a generalization of the concept of combinatorial $t$-schemes, which in this context corresponds to the case of commutative algebras. Balanced 2-systems are considered consisting of $v$ primitive idempotents in the matrix algebra $\mathrm M_n(\mathbb C)$, known as $(v,n)$-systems. It is proved that $(n+1,n)$-systems are unique and it is shown that there are no $(n+s,n)$-systems with $n>s^2-s$ or $s>n^2-n$. The $(q+1,n)$-systems having 2-transitive automorphism subgroup $PSL(2,q)$, $q$ odd, are classified. The (4,2)- and (6,3)-systems are classified. A balanced basis is constructed in the algebras $\mathrm M_n$, $n=2,3$. Connections are established between conference matrices and $(2n,n)$-systems, and between suitable matrices and $(m^2,\dfrac{m^2\pm m}2)$-systems.

DOI: https://doi.org/10.4213/sm471

Full text: PDF file (381 kB)
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English version:
Sbornik: Mathematics, 2000, 191:4, 543–565

Bibliographic databases:

UDC: 512.538+512.542+519.1
MSC: Primary 16P10, 05B20; Secondary 05B05, 62K10
Received: 12.05.1999

Citation: D. N. Ivanov, “Balanced systems of primitive idempotents in matrix algebras”, Mat. Sb., 191:4 (2000), 67–90; Sb. Math., 191:4 (2000), 543–565

Citation in format AMSBIB
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\by D.~N.~Ivanov
\paper Balanced systems of primitive idempotents in matrix algebras
\jour Mat. Sb.
\yr 2000
\vol 191
\issue 4
\pages 67--90
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\crossref{https://doi.org/10.4213/sm471}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1775043}
\zmath{https://zbmath.org/?q=an:1022.16017}
\transl
\jour Sb. Math.
\yr 2000
\vol 191
\issue 4
\pages 543--565
\crossref{https://doi.org/10.1070/sm2000v191n04ABEH000471}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-0034338866}


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  • http://mi.mathnet.ru/eng/msb/v191/i4/p67

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    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. Ivanov, DN, “Orthogonal decompositions and idempotent configurations in semisimple associative algebras”, Communications in Algebra, 29:9 (2001), 3839  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    2. D. N. Ivanov, “On balanced systems of idempotents”, Sb. Math., 192:4 (2001), 551–564  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. D. N. Ivanov, “On balanced bases”, Math. Notes, 77:2 (2005), 194–198  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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