anne.cortella@univ-fcomte.fr, david.lewis@ucd.ie

Submission: 2009, Mar 10

We define a notion of Morita equivalence between algebras with antiautomorphisms such that two equivalent algebras have the same category of sesquilinear forms. This generalizes the Morita equivalence of algebras with involutions defined by Fr\"olich and Mc Evett \cite{FMcE}, and their categories of $\varepsilon$-hermitian forms. For two Morita equivalent algebras with involution, with an additional technical property (which is true for central simple algebras), we define a new algebra with antiautomorphism, called the orthogonal sum, which generalizes the usual notion of orthogonal sum of forms. We explore the invariants of this sum.

2000 Mathematics Subject Classification: Primary 16W10; Secondary 16K20

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