On the index of nonlocal elliptic operators for compact Lie groups |
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Authors: | Anton Yu Savin |
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Institution: | 1.Faculty of Science,Peoples Friendship University of Russia,Moscow,Russia;2.Institute of Analysis,Leibniz University of Hannover,Hannover,Germany |
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Abstract: | We consider a class of nonlocal operators associated with a compact Lie group G acting on a smooth manifold. A notion of symbol of such operators is introduced and an index formula for elliptic elements
is obtained. The symbol in this situation is an element of a noncommutative algebra (crossed product by G) and to obtain an index formula, we define the Chern character for this algebra in the framework of noncommutative geometry. |
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