Illinois Journal of Mathematics

Hermitian Morita equivalences between maximal orders in central simple algebras

Bhanumati Dasgupta

Abstract

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

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

Dates
First available in Project Euclid: 4 October 2010

https://projecteuclid.org/euclid.ijm/1286212912

Digital Object Identifier
doi:10.1215/ijm/1286212912

Mathematical Reviews number (MathSciNet)
MR2727351

Zentralblatt MATH identifier
1204.15007

Subjects
Primary: 15A04: Linear transformations, semilinear transformations

Citation

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

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