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Hadamard algebras possessing the unique noncommutative simple component

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Abstract

The famous conjecture on the orders of Hadamard matrices can be reformulated as follows: a commutative algebra is Hadamard if and only if its dimension is divisible by 4. In this paper we study the Hadamard algebras closed to commutative ones, namely, the algebras possessing the unique noncommutative simple component being the matrix algebra of order 2.

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References

  1. D. N. Ivanov, “The Dimension of a Hadamard Algebra is Divisible by 4,” Uspekhi Matem Nauk 60(2), 163 (2005) [Russian Math. Surveys 60 (2), 357 (2005)].

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  2. D. N. Ivanov, “Orthogonal Decompositions of Associative Algebras, and Balanced Systems of Idempotents,” Matem. Sborn. 189(12), 83 (1998) [Sbornik: Math. 189 (12), 1819 (1998)].

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Authors and Affiliations

  1. Faculty of Mathematics, Tver State University, Zhelyabova st. 33, Tver, 170100, Russia

    D. N. Ivanov

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  1. D. N. Ivanov
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Original Russian Text © D.N. Ivanov, 2011, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2011, Vol. 66, No. 5, pp. 46–48.

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Ivanov, D.N. Hadamard algebras possessing the unique noncommutative simple component. Moscow Univ. Math. Bull. 66, 213–214 (2011). https://doi.org/10.3103/S0027132211050068

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  • DOI: https://doi.org/10.3103/S0027132211050068

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