dc.contributor.advisor | Park, Efton | |
dc.contributor.author | Hellerman, Nathanael | en_US |
dc.date.accessioned | 2018-12-19T19:51:05Z | |
dc.date.available | 2018-12-19T19:51:05Z | |
dc.date.created | 2018 | en_US |
dc.date.issued | 2018 | en_US |
dc.identifier | aleph-005160262 | en_US |
dc.identifier.uri | https://repository.tcu.edu/handle/116099117/22833 | |
dc.description.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. | |
dc.format.extent | 1 online resource (iii, 81 pages). | en_US |
dc.format.medium | Format: Online | en_US |
dc.language.iso | eng | en_US |
dc.relation.ispartof | Texas Christian University dissertation | en_US |
dc.relation.ispartof | UMI thesis. | en_US |
dc.relation.ispartof | Texas Christian University dissertation. | en_US |
dc.subject.lcsh | Toeplitz operators. | en_US |
dc.subject.lcsh | Algebra. | en_US |
dc.title | Toeplitz operators with symbols from certain rotation algebras and their index formulas | en_US |
dc.type | Text | en_US |
etd.degree.department | Department of Mathematics | |
etd.degree.level | Doctoral | |
local.college | College of Science and Engineering | |
local.department | Mathematics | |
local.academicunit | Department of Mathematics | |
dc.type.genre | Dissertation | |
local.subjectarea | Mathematics | |
etd.degree.name | Doctor of Philosophy | |
etd.degree.grantor | Texas Christian University | |