Department of Mathematical Sciences
Colloquium Series
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Division algebras over fields of characteristic p
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Kelly McKinnie
Rice University
Open Search Candidate |
The real Hamilton quaternions form a four dimensional real vector space with an associative multiplication and an identity element such that every nonzero element has a multiplicative inverse. In fact, this is the only such non-trivial finite dimensional division algebra that exists over the real numbers. The Hamiltonians are an example of a cyclic algebra. If you ask which division algebras occur over the rational numbers you get a plethora of different division algebras, yet they are all still cyclic algebras.
The situation changes slightly when you look for division algebras with dimension pn over a field of characteristic p. In this talk I will discuss characterizations of cyclic algebras along with examples of non-cyclic algebras over a field of characteristic p which remain non-cyclic after any prime to p extension.
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Thursday, 14 February 2008
4:10 p.m. in Math 103
3:30 p.m. Refreshments in Math Lounge 109
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