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Toeplitz operators with symbols from certain rotation algebras and their index formulas
Hellerman, Nathanael
Hellerman, Nathanael
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Date
2018
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Abstract
Let C(S^1) x Zn be the crossed product algebra, where the group Zn enacts a rotation on the complex coordinate z. We consider the algebra of Toeplitz operators with symbols from the crossed product algebra C(S^1) x Zn. We find the K-theory of this Toeplitz algebra and a formula to calculate the Fredholm index of an operator from it. Similarly, we consider the crossed product algebra of C(S^3) x Zn, where the group Zn enacts a rotation on one of the complex coordinates of S^3. We consider the algebra of Toeplitz operators with symbols from the crossed product algebra C(S^3) x Zn. We find the K-theory of this Toeplitz algebra and a formula to calculate the Fredholm index of an operator from it. The index formula is the sum of n integrals which can be used to determine when two operators are in different homotopy classes, even if they have the same index.
Contents
Subject
Subject(s)
Toeplitz operators.
Algebra.
Algebra.
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Genre
Dissertation
Description
Format
1 online resource (iii, 81 pages).
Department
Mathematics