## Toeplitz operators with symbols from certain rotation algebras and their index formulasShow full item record

Title | Toeplitz operators with symbols from certain rotation algebras and their index formulas |
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Author | Hellerman, Nathanael |

Date | 2018 |

Genre | Dissertation |

Degree | Doctor of Philosophy |

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. |

Link | https://repository.tcu.edu/handle/116099117/22833 |

Department | Mathematics |

Advisor | Park, Efton |

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##### This item appears in the following Collection(s)

- Doctoral Dissertations [1513]

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