RESEARCH ARTICLE

Some (Hopf) algebraic properties of circulant matrices

Helen Albuquerque^a, Florin Panaite<sup>b

a</sup> Departamento de Matemática, Universidade de Coimbra, 3001-454 Coimbra, Portugal
^b Institute of Mathematics of the Romanian Academy, PO-Box 1-764, RO-014700 Bucharest, Romania

Abstract: 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.

MSC: 15B05; 16W30

Received: 03.12.2011
Accepted: 03.12.2011

Language: English

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