Advanced search options

Advanced Search Options 🞨

Browse by author name (“Author name starts with…”).

Find ETDs with:

in
/  
in
/  
in
/  
in

Written in Published in Earliest date Latest date

Sorted by

Results per page:

Language: English

You searched for subject:(moyal). One record found.

Search Limiters

Last 2 Years | English Only

No search limiters apply to these results.

▼ Search Limiters

1. Gao, Li. On quantum Euclidean spaces: Continuous deformation and pseudo-differential operators.

Degree: PhD, Mathematics, 2018, University of Illinois – Urbana-Champaign

Quantum Euclidean spaces are noncommutative deformations of Euclidean spaces. They are prototypes of locally compact noncommutative manifolds in Noncommutative Geometry. In this thesis, we study the continuous deformation and Pseudo-differential calculus of quantum Euclidean spaces. After reviewing the basic definitions and representation theory of quantum Euclidean spaces in Chapter 1, we prove in Chapter 2 a Lip^(1/2) continuous embedding of the family of quantum Euclidean spaces. This result is the locally compact analog of U. Haagerup and M. R\o rdom's work on Lip^(1/2) continuous embedding for quantum 2-torus. As a corollary, we also obtained Lip^(1/2) embedding for quantum tori of all dimensions. In Chapter 3, we developed a Pseudo-differential calculus for noncommuting covariant derivatives satisfying the Canonical Commutation Relations. Based on some basic analysis on quantum Euclidean spaces, we introduce abstract symbol classs following the idea of abstract pseudo-differential operators introduced by A. Connes and H. Moscovici. We proved the two main ingredients pseudo-differential calculus  – the L2-boundedness of 0-order operators and the composition identity. We also identify the principal symbol map in our setting. Chapter 4 is devoted to application in the local index formula in noncommutative Geometry. We show that our setting with noncommuting covariant derivatives is an example of locally compact noncommutative manifold. After developed the Getzler super-symmetric symbol calculus, we calculate the local index formula for the a noncommutative analog of Bott projection. Advisors/Committee Members: Junge, Marius (advisor), Ruan, Zhong-Jin (Committee Chair), Boca, Florin P. (committee member), Oikhberg, Timur (committee member).

Subjects/Keywords: Noncommutative Euclidean spaces; Moyal Deformation; Pseudo-differential operators

…the parameter h, h being a deformation parameter. The Moyal product, depending gives a… …x5D;. In the rst part of this thesis, we study the continuity of Moyal deformation, or more… …space, which are called Moyal planes as in [15]. Because of its motivation from… …equivalent to the Moyal θ, −d Z Z λθ (f )λθ (g) = λθ (f ?θ g)… …x29; Rd Rd 7 The Moyal product is bilinear, associative and reversed under complex… 

Page 1 Page 2 Page 3 Page 4 Page 5 Page 6 Page 7

Record DetailsSimilar RecordsGoogle PlusoneFacebookTwitterCiteULikeMendeleyreddit

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Gao, L. (2018). On quantum Euclidean spaces: Continuous deformation and pseudo-differential operators. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/101546

Chicago Manual of Style (16th Edition):

Gao, Li. “On quantum Euclidean spaces: Continuous deformation and pseudo-differential operators.” 2018. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed April 13, 2021. http://hdl.handle.net/2142/101546.

MLA Handbook (7th Edition):

Gao, Li. “On quantum Euclidean spaces: Continuous deformation and pseudo-differential operators.” 2018. Web. 13 Apr 2021.

Vancouver:

Gao L. On quantum Euclidean spaces: Continuous deformation and pseudo-differential operators. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2018. [cited 2021 Apr 13]. Available from: http://hdl.handle.net/2142/101546.

Council of Science Editors:

Gao L. On quantum Euclidean spaces: Continuous deformation and pseudo-differential operators. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2018. Available from: http://hdl.handle.net/2142/101546

.