Abstract
Let R be a semilocal Bézout domain with fraction field F. Assume that 2 is invertible in R. The main result of this article states that R−algebras with involution that become isomorphic over F are already isomorphic over R. We also show that this implies that hermitian or skew-hermitian spaces over an R−algebra with involution without zero divisors that become similar over F, are already similar over R.
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Presented by Michel Van den Bergh.
First author: PhD Fellow of the Research Foundation - Flanders (FWO)
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Beke, S., Van Geel, J. An Isomorphism Problem for Azumaya Algebras with Involution over Semilocal Bézout Domains. Algebr Represent Theor 17, 1635–1655 (2014). https://doi.org/10.1007/s10468-013-9463-6
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DOI: https://doi.org/10.1007/s10468-013-9463-6
Keywords
- Azumaya algebras with involution
- Central simple algebras with involution
- Algebraic groups
- Valuation rings
- Semilocal Bézout domains
- (skew-)hermitian spaces
- Bilinear spaces
- Multipliers