On the Projective Schur Group of a Field

✍ Scribed by E. Aljadeff; J. Sonn

• Publisher: Elsevier Science
• Year: 1995
• Tongue: English
• Weight: 514 KB
• Volume: 178
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.1995.1364

✦ Synopsis

If (k) is a field, the projective Schur group (\operatorname{PS}(k)) of (k) is the subgroup of the Brauer group (\operatorname{Br}(k)) consisting of those classes which contain a projective Schur algebra, i.e., a homomorphic image of a twisted group algebra (k^{\text {" }} G) with (G) finite, (\alpha \in H^{2}\left(G, k^{*}\right)). It has been conjectured by Nelis and Van Oystaeyen ( (J). Algebra (137(1991), 501-518)) that (\operatorname{PS}(k)=\operatorname{Br}(k)) for all fields (k). We disprove this conjeclure by showing that (\mathrm{PS}(k) \neq \mathrm{Br}(k)) for rational function fields (k_{10}(x)) where (k_{0}) is any infinite field which is finitely generated over its prime field. to 1995 Academic Press, Inc.