Illinois Journal of Mathematics
- Illinois J. Math.
- Volume 53, Number 3 (2009), 723-736.
Hermitian Morita equivalences between maximal orders in central simple algebras
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.
Illinois J. Math., Volume 53, Number 3 (2009), 723-736.
First available in Project Euclid: 4 October 2010
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Mathematical Reviews number (MathSciNet)
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. https://projecteuclid.org/euclid.ijm/1286212912