Preprints and recent papers

• Available as pdf, dvi or postscript files below, or on the arXiv (most papers written since 2000 have been posted on the arXiv)

• Derivations and the first Hochschild cohomology group of the quantum grassmannian, with Stéphane Launois
  Click here for .pdf file or here for arXiv version

• Factorisation of cross-symmetric, totally nonnegative matrices and an amazing matrix, with Andrew Neate
  Click here for .pdf file or here for arXiv version

• The traces of quantum powers commute, with Matyas Domokos
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• The automorphism group of the quantum grassmannian, with Stéphane Launois, Bulletin of the London Mathematical Society 56 (2024), 1310–1327
  Click here for .pdf file or here for arXiv version or here for the journal article

• Total positivity is a quantum phenomenon: the grassmannian case, with Stéphane Launois and Brendan Nolan, Memoirs of the AMS, vol. 291, Amer. Math. Soc., Providence, RI, 2023, pp. 1-109
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• Generalised quantum determinantal rings are maximal orders, with Laurent Rigal, Glasgow Mathematical Journal 63 (2021), 515-525, DOI:10.1017/S001708952000035X
  Click here for .pdf file or here for xxx archive or here for the journal article

• Prime factors of quantum Schubert cell algebras and clusters for quantum Richardson varieties, with Milen Yakimov, J. Reine Angew. Math. 750 (2019), 123–156, DOI: 10.1515/crelle-2016-0046
  Click here for .pdf file or here for xxx archive or here for the journal article. (The versions here and on the arxiv contain more detail than the version published in Crelle.)

• Tauvel's height formula for quantum nilpotent algebras, with Ken Goodearl and Stéphane Launois, Communications in Algebra 47 (2019), no 10, 4194-4209, DOI: 10.1080/00927872.2019.1581210
  Click here for .pdf file or here for xxx archive or here for the journal article

• From totally nonnegative matrices to quantum matrices and back, via Poisson geometry, with Stéphane Launois, Perspectives in Lie theory, 443 - 461, Springer INdAM Ser., 19, Springer, Cham, 2017
  Click here for .pdf file or here for xxx archive (the arxiv version is an older, longer, version).

• Leavitt path algebras satisfying a polynomial identity, with Jason Bell and Kulumani Rangaswamy, Journal of Algebra and Its Applications Vol. 15, No. 5 (2016) 1650084, DOI: 10.1142/S0219498816500845
  Click here for .pdf file or here for xxx archive or here for the journal article

• Efficient recognition of totally nonnegative matrix cells, with Stéphane Launois, Foundations of Computational Mathematics 14 (2014), 371-387
  Click here for .pdf file or here for xxx archive or here for the journal article

• Automorphisms of quantum matrices, with Stéphane Launois, Glasgow Mathematical Journal 55A (2013), 89-100
  Click here for .pdf file or here for xxx archive or here for the journal article

• Nil algebras with restricted growth, with Agata Smoktunowicz and Alexander Young, Proceedings of the Edinburgh Mathematical Society 55 (2012), 461-475
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• LU decomposition of totally nonnegative matrices, with Ken Goodearl, Linear Algebra and its Applications, 436 (2012), 2554-2566
  Click here for .pdf file or here for xxx archive or here for the journal article

• Primitive ideals in quantum SL(3) and GL(3), with Ken Goodearl, Proceedings of the conference New Trends in Noncommutative Algebra, AMS Contemporary Maths, 562 (2012), 115-140
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• Twisting the quantum grassmannian, with Stéphane Launois, Proc Amer Math Soc 139 (2011), 99-110
  Click here for .pdf file or here for xxx archive or here for the journal article

• Totally nonnegative cells and matrix Poisson varieties, with Ken Goodearl and Stéphane Launois, Advances in Mathematics 226 (2011) 779-826.
  Click here for .pdf file or here for xxx archive or here for the journal article
  A pdf file of the published version is available on request from the authors.

• Torus-invariant prime ideals in quantum matrices, totally nonnegative cells and symplectic leaves, with Ken Goodearl and Stéphane Launois, Mathematische Zeitschrift 269 (2011), 29-45 (doi:10.1007/s00209-010-0714-5)
  Click here for .pdf file or here for xxx archive or here for the journal article

• Mini-Workshop: Non-Negativity is a Quantum Phenomenon, Organized by: Stéphane Launois and Thomas H. Lenagan, Oberwolfach Reports (2009) Vol 6, Issue 1, 767--800
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• Cyclic orders on the quantum grassmannian, with Ewan Russell, Arabian Journal for Science and Engineering (Section C: theme issue -- Interactions of algebraic and coalgebraic structures), 33 (2008), 337-350
  Click here for .pdf file or here for xxx archive or here for the journal article

• Quadratic and cubic invariants of unipotent affine automorphisms, with Vladimir Bavula, Journal of Algebra 320 (2008) 4132-4155
  Click here for .pdf file or here for xxx archive

• Prime ideals in the quantum grassmannian, with Stéphane Launois and Laurent Rigal, Selecta Mathematica 13 (2008), 697-725
  Click here for .pdf file or here for xxx archive

• Quantum analogues of Schubert varieties in the grassmannian, with Laurent Rigal, Glasgow Mathematical Journal 50 (2008), 55-70
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• An infinite dimensional affine nil algebra with finite Gelfand-Kirillov dimension, with Agata Smoktunowicz, Journal of the American Mathematical Society, 20 (2007), 989-1001
  Click here for .pdf file or here for xxx archive or here for the journal article

• The first Hochschild cohomology group of quantum matrices and the quantum special linear group, with Stéphane Launois, Journal of Noncommutative Geometry 1 (2007), 281-309
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• Quantised coordinate rings of semisimple groups are unique factorisation domains, with Stéphane Launois, Bulletin of the London Mathematical Society 39 (2007), 433--438
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• Primitive ideals and automorphisms of quantum matrices, with Stéphane Launois, Algebras and Representation Theory 10 (2007), 339-365
  Click here for .pdf file or here for xxx archive

• Quantum unique factorisation domains, with Stéphane Launois and Laurent Rigal, J London Math Soc 74 (2006), 321-340
  Click here for .pdf file or here for xxx archive

• Quantum graded algebras with a straightening law and the AS-Cohen-Macaulay property for quantum determinantal rings and quantum grassmannians, with Laurent Rigal, J Algebra 301 (2006) 670-702
  Click here for .pdf or here for xxx archive. Please note that there are slight changes between the arxiv version and the published paper. The .pdf version here corresponds to the published version.

• Quantized trace rings, with Matyas Domokos, Quarterly Journal of Maths 56 (2005), 507-523
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• Quantized coinvariants at transcendental q, with Ken Goodearl, in Hopf algebras in noncommutative geometry and physics, 155--165, Lecture Notes in Pure and Appl. Math., 239, Dekker, New York, 2005
  Click here for .pdf file or here for xxx archive

• Representation rings of quantum groups, with Matyas Domokos, Journal of Algebra 282 (2004), 103-128
  Click here for .pdf file or here for xxx archive

• Ring theoretic properties of quantum grassmannians, with Ann Kelly and Laurent Rigal, Journal of Algebra and its Applications 3 (2004), 9-30
  Click here for .pdf file or here for xxx archive
  Click here for Corrigenda, 3 (2004) 219

• The maximal order property for quantum determinantal rings, with Laurent Rigal, Proceedings of the Edinburgh Mathematical Society 46 (2003), 513-529
  Click here for .pdf file or here for xxx archive

• Weakly multiplicative coactions of quantized function algebras, with Matyas Domokos, Journal of Pure and Applied Algebra 183 (2003), 45-60
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• Orbits for the adjoint coaction on quantum matrices, with Matyas Domokos and Rita Fioresi, Journal of Geometry and Physics 47 (2003), 447-468
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• Winding invariant prime ideals in quantum 3x3 matrices, with Ken Goodearl, Journal of Algebra 260 (2003), 657-687
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• Conjugation coinvariants of quantum matrices, with Matyas Domokos, Bulletin of the London Mathematical Society 35 (2003), 117-127
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• Prime ideals invariant under winding automorphisms in quantum matrices, with Ken Goodearl, International Journal of Mathematics 13 (2002), 497-532
  Click here for .pdf file or here for xxx archive

• Dimensions of quantum determinantal rings, with Laurent Rigal, Glasgow Math. Journal 44 (2002), 285-292
  Click here for .pdf file or here for the journal article

• Generalized Weyl Algebras are Tensor Krull Minimal, with Vladimir Bavula, Journal of Algebra 239 (2001), 93-111
  Click here for .pdf file

• Krull dimension of Generalised Weyl Algebras with noncommutative coefficients, with Vladimir Bavula, Journal of Algebra 235 (2001), 315-358
  Click here for .pdf file

• The First Fundamental Theorem of Coinvariant Theory for the Quantum General Linear Group, with Ken Goodearl and Laurent Rigal, Publ. Research Inst. Math. Sci. Kyoto 36 (2000), 269-296
  Click here for .ps file or here for .dvi file or here for xxx archive

• Poincaré series of multifiltered algebras and partitivity, with José Gómez Torrecillas, J. London Math. Soc., 62 (2000), 370-380.
  Click here for .ps file or here for .dvi file

• Dimension theory of noetherian rings, Infinite length modules (Bielefeld, 1998), 129--147, Trends Math., Birkhduser, Basel, 2000
  Click here for .ps file or here for .dvi file

• Prime ideals in certain quantum determinantal rings, with Ken Goodearl, in Interactions between Ring Theory and Representations of Algebras (Murcia, 1998) (F. Van Oystaeyen and M. Saorin, Eds.), New York (2000) Dekker, pp. 239-251
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• Quantum Determinantal Ideals, with Ken Goodearl, Duke Math. J. 103 (2000) 165-190
  Click here for .pdf file or here for .dvi file

Growth of Algebras and Gelfand-Kirillov dimension, with Günter Krause

A revised edition of this book has been published by the American Mathematical Society:

Graduate Studies in Mathematics, 22. American Mathematical Society, Providence, RI, 2000. x+212 pp. ISBN: 0-8218-0859-1