Hopf algebras
Preferred learners
- Edmonton, Alberta, Canada
- Academic experience or paid work
Categories
Project scope
- What is the main goal for this project?
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For every locally compact abelian group G, the set of characters is also a locally compact abelian group and the Pontrjagin theorem says that the double dual is isomorphic to the original group G. For a non-abelian group, a generalized dual can no longer be defined in the form of a group. One has to look for a larger category, namely quantum groups in the form of Hopf algebras. The objective is to study Hopf algebras in the setting of C*-algebras and von Neumann algebras such that a generalization of Pontrjagin duality is obtained.
- What tasks will learners need to complete to achieve the project goal?
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The student will read about Hopf algebras, C*-algebras and von Neumann algebras. Although there is a vast literature, the student will focus on a textbook and several articles that complement the book.
- What is the main goal for this project?
-
For every locally compact abelian group G, the set of characters is also a locally compact abelian group and the Pontrjagin theorem says that the double dual is isomorphic to the original group G. For a non-abelian group, a generalized dual can no longer be defined in the form of a group. One has to look for a larger category, namely quantum groups in the form of Hopf algebras. The objective is to study Hopf algebras in the setting of C*-algebras and von Neumann algebras such that a generalization of Pontrjagin duality is obtained.
- What tasks will learners need to complete to achieve the project goal?
-
The student will read about Hopf algebras, C*-algebras and von Neumann algebras. Although there is a vast literature, the student will focus on a textbook and several articles that complement the book.
- How will you support learners in completing the project?
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I will help the student through discussion either in person of via email.
About the company
- https://www.macewan.ca/academics/academic-departments/mathematics-statistics/
- 0 - 1 employees
- Education
The Department of Mathematics and Statistics provides a vibrant and supportive home base for students who want to study mathematics and statistics. Our growing department is home to excellent scholars and has a deep commitment to student success, whether taking math as a requirement or as a pursuit of passion. Our faculty members are dedicated to providing an education that emphasizes the knowledge and broad analytical skills that are valuable in today’s world.
Beyond the classroom, our department organizes Torus Talks, a regular presentation series where faculty and students share insights into the uses and versatility of mathematics and statistics, and a Math Help Centre, where students can access additional support in mastering their course work.
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