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\textsc{Algebra}
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\textsc{Seminar}
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\textit{Involutions and crossed products}
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David Saltman\par
University of Texas
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\textbf{Abstract:} One approach to studying central simple algebras with involutions is to
start by studying the generic algebras with generic involutions. It seems that some
of the properties of these generic cases is encoded in the structure of their center.
These centers can be written as multiplicative invariant fields of finite groups. More
specifically, these centers have the form $F(M)^G$ where $G$ is a finite group and $M$ is
a lattice over $G$. This then raises the question: What do finite groups and lattices
have to do with involutions? The ``answer'' we will try and give begins with old
work about involutions and Severi-Brauer varieties, and involves what I call ``well
situated'' involutions with respect to a subfield.\vspace{\fill}
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Friday, April 27, 2007, 4:00 pm\par
Mathematics and Science Center, W303
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\textsc{Mathematics and Computer Science}\par
\textsc{Emory University}
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