Commutative power-associative representations of symmetric matrices

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Commutative power-associative representations of symmetric matrices

Murakami, Lucia S.I.; Nascimento, Pablo S.M.; Shestakov, Ivan; Picanço da Silva, Juaci

Journal of algebra, 04/2024, Volume: 644

Journal Article

The classification of irreducible unital commutative power-associative modules for Hn(F), the algebra of symmetric matrices with the Jordan product, over a field F of characteristic not 2, 3 and 5 are given, for n≥3. It is proved that there exists, up to isomorphisms, only one irreducible module which is not Jordan. It is also shown that every finite dimensional unital commutative power associative module for this algebra is completely reducible.

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Murakami, Lucia S.I. | Nascimento, Pablo S.M. | Shestakov, Ivan | Picanço da Silva, Juaci

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