Professor Jan Grabowski CMath FIMA SFHEA

Professor of Algebra

Research Overview

My research is in the area of quantum algebra. Here "algebra" refers to the major branch of mathematics that studies the structure of mathematical objects and their symmetries. The adjective "quantum" highlights a relationship with the quantum theory of physics. In the mathematics of that theory, many of the variables do not commute - that is, a times b need not equal b times a. Many of the structures in quantum algebra have a multiplication that is not commutative. The ones I study are often not far from being commutative, though. One can often deform a commutative product of two elements a and b by putting in an extra parameter, q say, and changing the product so that now ab=qba. Then ba=(1/q)ab and if q does not equal 1, the product is not commutative. We can think of being allowed to vary q and talk of q=1 as the "classical limit", just as classical physics can be recovered from quantum physics. The study of these deformations of well-understood classical algebraic and geometric objects is what makes up the field of quantum algebra.

More specifically, I work with Lie algebras, quantized enveloping algebras, quantized coordinate rings, partial flag varieties and quantum cluster algebras.

Selected Publications


Grabowski, J., Hindmarch, L. 5/12/2024 In: Bulletin of the London Mathematical Society. 56, 12, p. 3777-3785. 9 p.
Journal article


Grabowski, J., Hone, A., Kim, W. 28/02/2024 In: arxiv.org. 40 p.
Journal article


Cooney, N., Grabowski, J. 7/02/2020 In: arxiv.org. 7 p.
Journal article


Cooney, N., Grabowski, J.E. 15/08/2022 In: Journal of Algebra. 604, p. 296-323. 28 p.
Journal article


Grabowski, J.E., Pressland, M. 1/01/2018 In: Documenta Mathematica. 23, p. 49-76. 23 p.
Journal article


Grabowski, J.E., Gratz, S. 11/2018 In: Journal of Pure and Applied Algebra. 222, 11, p. 3395-3413. 18 p.
Journal article


Grabowski, J. 12/2015 In: Journal of Algebraic Combinatorics. 42, 4, p. 1111-1134. 24 p.
Journal article


Grabowski, J., Launois, S. 23/05/2014 In: Proceedings of the London Mathematical Society. 109, 3, p. 697-732. 36 p.
Journal article


Grabowski, J., Gratz, S., Groechenig, M. 04/2014 In: Journal of the London Mathematical Society. 89, 2, p. 337-363. 27 p.
Journal article


Allman, J.M., Grabowski, J. 06/2012 In: Journal of Algebra. 359, 1, p. 49-68. 20 p.
Journal article


Grabowski, J., Launois, S. 2011 In: International Mathematics Research Notices. 2011, 10, p. 2230-2262. 33 p.
Journal article


Grabowski, J. 2011 In: Journal of Pure and Applied Algebra. 215, 7, p. 1582-1595. 14 p.
Journal article


Grabowski, J. 14/10/2011 In: Communications in Algebra. 39, 10, p. 3491-3514. 24 p.
Journal article


Grabowski, J. 2008 In: Journal of Lie Theory. 18, 1, p. 125-140. 16 p.
Journal article


Grabowski, J. 2006 University of London.
Doctoral Thesis


Grabowski, J. 2005 In: Journal of Algebra and Its Applications. 4, 6, p. 707-737. 30 p.
Journal article


Grabowski, J. 2005 In: Pacific Journal of Mathematics. 221, 2, p. 281-301. 22 p.
Journal article


04/01/2022 → 31/12/2022
Research


20/01/2020 → 19/01/2022
Research


01/12/2018 → 30/11/2020
Research


28/11/2014 → 27/03/2016
Research


School Engagement


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Visiting an external academic institution


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Hosting an academic visitor


Participation in conference -Mixed Audience


Participation in conference -Mixed Audience


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Hosting an academic visitor


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Publication peer-review


Publication peer-review


Hosting an academic visitor


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Hosting an academic visitor


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Hosting an academic visitor


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Editorial activity


Invited talk


Hosting an academic visitor


Invited talk


Membership of committee


Publication peer-review


School Engagement


Membership of committee


Publication peer-review


Membership of committee


Membership of committee


Participation in conference -Mixed Audience


Participation in conference -Mixed Audience


Publication peer-review


Participation in workshop, seminar, course


Participation in workshop, seminar, course


Hosting an academic visitor


Participation in workshop, seminar, course


Participation in conference -Mixed Audience

  • Algebra and Geometry
  • Mathematical Physics (Maths and Stats)