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Some (Hopf) algebraic properties of circulant matrices
Algebra and discrete mathematics, Tome 13 (2012) no. 1, pp. 1-17 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study some (Hopf) algebraic properties of circulant matrices, inspired by the fact that the algebra of circulant $n\times n$ matrices is isomorphic to the group algebra of the cyclic group with $n$ elements. We introduce also a class of matrices that generalize both circulant and skew circulant matrices, and for which the eigenvalues and eigenvectors can be read directly from their entries.
Keywords: Hopf algebras; (generalized) circulant matrices; Brandt algebras. 
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Helen Albuquerque; Florin Panaite. Some (Hopf) algebraic properties of circulant matrices. Algebra and discrete mathematics, Tome 13 (2012) no. 1, pp. 1-17. http://geodesic.mathdoc.fr/item/ADM_2012_13_1_a1/

[1] H. Albuquerque, R. S. Krausshar, “Multiplicative invariant lattices in ${\mathbb R}^n$ obtained by twisting of group algebras and some explicit characterizations”, J. Algebra, 319 (2008), 1116–1131 | DOI | MR | Zbl

[2] A. Cap, H. Schichl, J. Vanžura, “On twisted tensor products of algebras”, Comm. Algebra, 23 (1995), 4701–4735 | DOI | MR | Zbl

[3] P. J. Davis, Circulant Matrices, John Wiley, New York, 1977 | MR

[4] S. Montgomery, Hopf Algebras and Their Actions on Rings, CBMS Reg. Conf. Series, 82, Providence, RI, 1993 | MR

[5] J. C. Waterhouse, “The structure of monomial circulant matrices”, SIAM J. Alg. Disc. Meth., 8 (1987), 467–482 | DOI | MR | Zbl