Geodesic
Hadamard Decompositions of Nearly Commutative Algebras
Matematičeskie zametki, Tome 103 (2018) no. 4, pp. 536-543

Voir la notice de l'article provenant de la source Math-Net.Ru

The notion of Hadamard decomposition of a semisimple associative finite-dimensional complex algebra generalizes the notion of the classical Hadamard matrix, which corresponds to the case of a commutative algebra. Algebras admitting Hadamard decompositions are said to be Hadamard. The paper considers the structure of Hadamard decompositions of algebras all of whose irreducible characters are of degree $1$ except one character of degree $2$. In particular, it is shown how to construct an Hadamard matrix of order $n$ by using the Hadamard decomposition of such an algebra of dimension $n$.
Mots-clés : orthogonal decomposition, Hadamard algebra, Hadamard matrix. 
@article{MZM_2018_103_4_a4,
     author = {D. N. Ivanov},
     title = {Hadamard {Decompositions} of {Nearly} {Commutative} {Algebras}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {536--543},
     publisher = {mathdoc},
     volume = {103},
     number = {4},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2018_103_4_a4/}
}
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D. N. Ivanov. Hadamard Decompositions of Nearly Commutative Algebras. Matematičeskie zametki, Tome 103 (2018) no. 4, pp. 536-543. http://geodesic.mathdoc.fr/item/MZM_2018_103_4_a4/