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Functional Identities on Matrix Algebras

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Complete solutions of functional identities \({\sum }_{k\in K}F_{k}\left (\overline {x}_{m}^{k}\right )x_{k} = {\sum }_{l\in L}x_{l}G_{l}\left (\overline {x}_{m}^{l}\right )\) on the matrix algebra M n (\(\mathbb {F}\)) are given. The nonstandard parts of these solutions turn out to follow from the Cayley-Hamilton identity.

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Correspondence to Špela Špenko.

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Presented by Vlastimil Dlab.

Supported by ARRS Grant P1-0288.

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Brešar, M., Špenko, Š. Functional Identities on Matrix Algebras. Algebr Represent Theor 18, 1337–1356 (2015).

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Mathematics Subject Classification (2010)