Illinois Journal of Mathematics

Hermitian Morita equivalences between maximal orders in central simple algebras

Bhanumati Dasgupta

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Let R be a Dedekind domain with quotient field $K$. That every maximal order in a finite dimensional central simple $K$-algebra $A$, (the algebra of nxn matrices over $D$), where $D$ is separable over $K$, is Morita equivalent to every maximal order in $D$ is a well known linear result. Hahn defined the notion of Hermitian Morita equivalence (HME) for algebras with anti-structure, generalizing previous work by Frohlich and McEvett. The question this paper investigates is the hermitian analogue of the above linear result. Specifically, when are maximal orders with anti-structure in $A$, HME to maximal orders with anti-structure in $D$ in the sense of Hahn? Two sets of necessary and sufficient conditions are obtained with an application which provides the hermitian analogue under some conditions.

Article information

Illinois J. Math., Volume 53, Number 3 (2009), 723-736.

First available in Project Euclid: 4 October 2010

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Zentralblatt MATH identifier

Primary: 15A04: Linear transformations, semilinear transformations


Dasgupta, Bhanumati. Hermitian Morita equivalences between maximal orders in central simple algebras. Illinois J. Math. 53 (2009), no. 3, 723--736. doi:10.1215/ijm/1286212912.

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