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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
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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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http://mi.mathnet.ru/eng/msb471https://doi.org/10.4213/sm471 http://mi.mathnet.ru/eng/msb/v191/i4/p67
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This publication is cited in the following articles:
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Ivanov, DN, “Orthogonal decompositions and idempotent configurations in semisimple associative algebras”, Communications in Algebra, 29:9 (2001), 3839
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D. N. Ivanov, “On balanced systems of idempotents”, Sb. Math., 192:4 (2001), 551–564
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D. N. Ivanov, “On balanced bases”, Math. Notes, 77:2 (2005), 194–198
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