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Operator Algebras and their Applications
School of Mathematics, IPM
Speaker:
Mostafa Esfahani Zadeh
IASBS, Zanjan
Topological $K$-Theory of C*-algebras
Abstract:
The subject of these lectures is the topological $K$-theory of
$C^*$-algebras. In a geometric view point, $K$-groups arise
naturally as the carrying space for the index of elliptic operators
satisfying some additional symmetries. In these lectures we begin by
a brief discussion of the $K$-theory for a locally compact Hausdorff
space that leads us naturally to the definition of the $K$-groups of
an arbitrary $C^*$-algebras. Then, using this definition, we compute
$K$-groups for some simple algebras and prove some elementary
properties of these groups. Perhaps the most important theorem in
elementary theory of $K$-theory is, the so called, {\it Cyclic six
term exact sequence}. We clarify and explain this theorem and
investigate some spacial case as final aim of our lectures.
Information:
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Time: | Wed. April 11, 2007, 14:00-16:00
Wed. April 18, 2007, 15:00-17:00
Wed. April 25, 2007, 15:00-17:00
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| Place: | Niavaran Bldg., Niavaran Square, Tehran, Iran |
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