| EPSRC Reference: |
EP/K035827/1 |
| Title: |
Total nonnegativity, quantum algebras and growth of algebras |
| Principal Investigator: |
Lenagan, Professor T |
| Other Investigators: |
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| Researcher Co-Investigators: |
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| Project Partners: |
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| Department: |
Sch of Mathematics |
| Organisation: |
University of Edinburgh |
| Scheme: |
Overseas Travel Grants (OTGS) |
| Starts: |
01 July 2013 |
Ends: |
31 March 2015 |
Value (£): |
21,074
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| EPSRC Research Topic Classifications: |
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| EPSRC Industrial Sector Classifications: |
| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
This is wide ranging project that involves the three areas of noncommutative
algebra, Poisson algebraic geometry and linear algebra. Also, the solutions
often involve representation theory and combinatorics. In addition, the
project will consider problems concerning growth of algebras.
The development of the theory of quantum algebras was motivated by problems in
Physics from the 1980s onwards. Totally nonnegative matrices have been
involved in problems in such diverse areas as mechanical systems, birth and
death processes, planar resistor networks, computer aided geometric design,
juggling, etc. Results concerning growth of algebras have been obtained from
the 1960s onwards, but the subject was in a quiescent state until the 2000s
when significant advances have been made.
In the past five years, surprising links between the three areas mentioned in
the first paragraph have been discovered and investigated. A partial
understanding of these connections has been gained, especially in the particular
case of coordinate algebras of matrices. The present project aims to further
this understanding by deepening the knowledge of the matrix case and by
expanding the scope of the knowledge to include algebras such as
grassmannians, partial flag varieties and De Concini-Kac-Procesi algebras.
The growth part of the project will concentrate on two specific types of
growth: quadratic growth/Gelfand-Kirillov dimension two, and intermediate
growth (super polynomial, but subexponential).
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Key Findings |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Potential use in non-academic contexts |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Impacts |
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| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
| Summary |
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| Date Materialised |
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Sectors submitted by the Researcher |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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| Project URL: |
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| Further Information: |
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| Organisation Website: |
http://www.ed.ac.uk |