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

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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. 
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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/

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