Irreducible characters of Hadamard algebras

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• 作者：D. N. Ivanov
• 刊名：Mathematical Notes
• 出版年：2016
• 出版时间：May 2016
• 年：2016
• 卷：99
• 期：5-6
• 页码：879-885
• 全文大小：632 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Russian Library of Science
  
• 出版者：MAIK Nauka/Interperiodica distributed exclusively by Springer Science+Business Media LLC.
• ISSN：1573-8876
• 卷排序：99

文摘

The notion of Hadamard decomposition of a semisimple associative finite-dimensional complex algebra generalizes the notion of classicalHadamard matrix, which corresponds to the case of commutative algebras. The algebras admitting Hadamard decompositions are called Hadamard algebras. A relation for the values of an irreducible character of a Hadamard algebra on the products of involutions forming an orthogonal basis of the algebra is obtained. This relation is then applied to describe the Hadamard decompositions in an algebra of dimension 8.KeywordsHadamard algebraHadamard decompositionHadamard matrixirreducible character