Professor Ken Brown
- Emeritus Professor (School of Mathematics & Statistics)
email:
Ken.Brown@glasgow.ac.uk
R321C Level 3, Mathematics, Mathematics Building, Glasgow G12 8QW
https://orcid.org/0000-0003-3497-3372Research interests
My main research interests are in noncommutative algebra, more specifically the structure of noncommutative rings and algebras and of their representations. At present my focus is primarily on Hopf algebras, on quantum groups and on homological questions, but in the past I have worked on symplectic reflection algebras, on enveloping algebras, on rings of differential operators, on group rings, and on invariant rings, as well as on "abstract" noetherian ring theory, and I maintain an active interest in all these topics.
Research groups
Publications
Selected publications
Brown, K. A. and Zhang, J. J. (2010) Prime regular Hopf algebras of GK-dimension one. Proceedings of the London Mathematical Society, 101(1), pp. 260-302. (doi: 10.1112/plms/pdp060)
Brown, K.A. and Changtong, K. (2010) Symplectic reflection algebras in positive characteristic. Proceedings of the Edinburgh Mathematical Society, 53(1), pp. 61-81. (doi: 10.1017/S0013091507001435)
Brown, K.A., Gordon, I.G. and Stroppel, C. (2008) Cherednik, Hecke and quantum algebras as free Frobenius and Calabi–Yau extensions. Journal of Algebra, 319(3), pp. 1007-1034. (doi: 10.1016/j.jalgebra.2007.10.026)
Brown, K.A. and Zhang, J.J. (2008) Dualising complexes and twisted Hochschild (co)homology for noetherian Hopf algebras. Journal of Algebra, 320(5), pp. 1814-1850. (doi: 10.1016/j.jalgebra.2007.03.050)
All publications
2023
Brown, K. , Carvalho, P. A.A.B. and Matczuk, J. (2023) Critical and injective modules over skew polynomial rings. Journal of Pure and Applied Algebra, 227(11), 107441. (doi: 10.1016/j.jpaa.2023.107441)
Bell, J. P., Brown, K. , Nazemian, Z. and Smertnig, D. (2023) On noncommutative bounded factorization domains and prime rings. Journal of Algebra, 622, pp. 404-449. (doi: 10.1016/j.jalgebra.2023.01.023)
Brown, K.A. , Couto, M. and Jahn, A. (2023) The finite dual of commutative-by-finite Hopf algebras. Glasgow Mathematical Journal, 65(1), pp. 62-89. (doi: 10.1017/S0017089522000052)
2022
Brown, K. and Tabiri, A. A. (2022) Plane curves which are quantum homogenous spaces. Algebras and Representation Theory, 25(4), pp. 889-922. (doi: 10.1007/s10468-021-10052-y)
Brown, K. A. and Zhang, J. J. (2022) Iterated Hopf Ore extensions in positive characteristic. Journal of Noncommutative Geometry, 16(3), pp. 787-837. (doi: 10.4171/jncg/453)
2021
Brown, K.A. and Zhang, J.J. (2021) Survey on Hopf algebras of GK-dimension 1 and 2. Contemporary Mathematics, 771, pp. 43-62. (doi: 10.1090/conm/771/15507)
2019
Brown, K. , Carvalho, P. A.A.B. and Matczuk, J. (2019) Simple modules and their essential extensions for skew polynomial rings. Mathematische Zeitschrift, 291(3-4), pp. 877-903. (doi: 10.1007/s00209-018-2128-8)
Brown, K.A. , Gilmartin, P. and Zhang, J.J. (2019) Connected (graded) Hopf algebras. Transactions of the American Mathematical Society, 372, pp. 3283-3317. (doi: 10.1090/tran/7686)
2018
Brown, K.A. and Yakimov, M.T. (2018) Azumaya loci and discriminant ideals of PI algebras. Advances in Mathematics, 340, pp. 1219-1255. (doi: 10.1016/j.aim.2018.10.024)
Brown, K. A. and Zhang, J. J. (2018) Unimodular graded Poisson Hopf algebras. Bulletin of the London Mathematical Society, 50(5), pp. 887-898. (doi: 10.1112/blms.12194)
2017
Brown, K. A. and Macleod, M. J. (2017) The Cohen Macaulay property for noncommutative rings. Algebras and Representation Theory, 20(6), pp. 1433-1465. (doi: 10.1007/s10468-017-9694-z)
2015
Brown, K.A. , O'Hagan, S., Zhang, J.J. and Zhuang, G. (2015) Connected Hopf algebras and iterated Ore extensions. Journal of Pure and Applied Algebra, 219, pp. 2405-2443. (doi: 10.1016/j.jpaa.2014.09.007)
Brown, K. and Gilmartin, P. (2015) Quantum homogeneous spaces of connected Hopf algebras. Journal of Algebra, 454, pp. 400-432.
Brown, K. A. and Goodearl, K. R. (2015) Zariski topologies on stratified spectra of quantum algebras. In: Eisenbud, David (ed.) Commutative Algebra and Noncommutative Algebraic Geometry. Series: Mathematical sciences research institute publications, 68 (68). Cambridge University Press, pp. 63-91. ISBN 9781107149724
2014
Brown, K. and Gilmartin, P. (2014) Hopf algebras under finiteness conditions. Palestine Journal of Mathematics, 3(S1), pp. 356-365.
2013
Brown, K. and Macauley, M. (2013) Ambiskew Hopf algebras. Journal of Pure and Applied Algebra, 217(1), pp. 59-74. (doi: 10.1016/j.jpaa.2012.04.007)
2010
Brown, K.A. and Changtong, K. (2010) Symplectic reflection algebras in positive characteristic. Proceedings of the Edinburgh Mathematical Society, 53(1), pp. 61-81. (doi: 10.1017/S0013091507001435)
Brown, K. A. and Zhang, J. J. (2010) Prime regular Hopf algebras of GK-dimension one. Proceedings of the London Mathematical Society, 101(1), pp. 260-302. (doi: 10.1112/plms/pdp060)
2008
Brown, K.A. and Zhang, J.J. (2008) Dualising complexes and twisted Hochschild (co)homology for noetherian Hopf algebras. Journal of Algebra, 320(5), pp. 1814-1850. (doi: 10.1016/j.jalgebra.2007.03.050)
Brown, K.A., Gordon, I.G. and Stroppel, C. (2008) Cherednik, Hecke and quantum algebras as free Frobenius and Calabi–Yau extensions. Journal of Algebra, 319(3), pp. 1007-1034. (doi: 10.1016/j.jalgebra.2007.10.026)
2007
Ardakov, K. and Brown, K.A. (2007) Primeness, semiprimeness and localisation in Iwasawa algebras. Transactions of the American Mathematical Society, 359, pp. 1499-1515. (doi: 10.1090/S0002-9947-06-04153-5)
Brown, K. (2007) Noetherian Hopf algebras. In: Antalya Algebra Days, Antalya, Turkey, 22-27 May 2007,
2006
Brown, K.A., Goodearl, K.R. and Yakimov, M. (2006) Poisson structures on affine spaces and flag varieties. I. Matrix affine Poisson space. Advances in Mathematics, 206(2), pp. 567-629. (doi: 10.1016/j.aim.2005.10.004)
Ardakov, K. and Brown, K.A. (2006) Ring-theoretic properties of Iwasawa algebras: a survey. In: Fesenko, I. (ed.) A Collection of Manuscripts Written in Honour of John H. Coates on the Occasion of his Sixtieth Birthday. Series: Documenta mathematica: extra volume (4). Deutsche Mathematiker-Vereinigung: Bielefeld, Germany, pp. 7-33. ISBN 9783936609288
2005
Brown, K. (2005) Unruffled extensions and flatness over central subalgebras. Journal of Algebra, 284, pp. 771-800. (doi: 10.1016/j.jalgebra.2004.10.008)
2003
Brown, K. (2003) Symplectic reflection algebras. Bulletin of the Irish Mathematical Society, 50, pp. 27-49.
Brown, K. and Gordon, I. (2003) Poisson orders, symplectic reflection algebras and representation theory. Journal für die reine und angewandte Mathematik (Crelles Journal), 559, pp. 193-216.
2002
Brown, K.A. and Goodearl, K.R. (2002) Lectures on Algebraic Quantum Groups. Series: Advanced courses in mathematics, CRM Barcelona. Birkhäuser: Basel, Switzerland. ISBN 9783764367145
Brown, K. and Gordon, I. (2002) The ramifications of the centres: Quantised function algebras at roots of unity. Proceedings of the London Mathematical Society, 84, pp. 147-178.
2001
Brown, K. and Gordon, I. (2001) The ramification of centres: Lie algebras in positive characteristic and quantised enveloping algebras. Mathematische Zeitschrift, 238, pp. 733-779.
Articles
Brown, K. , Carvalho, P. A.A.B. and Matczuk, J. (2023) Critical and injective modules over skew polynomial rings. Journal of Pure and Applied Algebra, 227(11), 107441. (doi: 10.1016/j.jpaa.2023.107441)
Bell, J. P., Brown, K. , Nazemian, Z. and Smertnig, D. (2023) On noncommutative bounded factorization domains and prime rings. Journal of Algebra, 622, pp. 404-449. (doi: 10.1016/j.jalgebra.2023.01.023)
Brown, K.A. , Couto, M. and Jahn, A. (2023) The finite dual of commutative-by-finite Hopf algebras. Glasgow Mathematical Journal, 65(1), pp. 62-89. (doi: 10.1017/S0017089522000052)
Brown, K. and Tabiri, A. A. (2022) Plane curves which are quantum homogenous spaces. Algebras and Representation Theory, 25(4), pp. 889-922. (doi: 10.1007/s10468-021-10052-y)
Brown, K. A. and Zhang, J. J. (2022) Iterated Hopf Ore extensions in positive characteristic. Journal of Noncommutative Geometry, 16(3), pp. 787-837. (doi: 10.4171/jncg/453)
Brown, K.A. and Zhang, J.J. (2021) Survey on Hopf algebras of GK-dimension 1 and 2. Contemporary Mathematics, 771, pp. 43-62. (doi: 10.1090/conm/771/15507)
Brown, K. , Carvalho, P. A.A.B. and Matczuk, J. (2019) Simple modules and their essential extensions for skew polynomial rings. Mathematische Zeitschrift, 291(3-4), pp. 877-903. (doi: 10.1007/s00209-018-2128-8)
Brown, K.A. , Gilmartin, P. and Zhang, J.J. (2019) Connected (graded) Hopf algebras. Transactions of the American Mathematical Society, 372, pp. 3283-3317. (doi: 10.1090/tran/7686)
Brown, K.A. and Yakimov, M.T. (2018) Azumaya loci and discriminant ideals of PI algebras. Advances in Mathematics, 340, pp. 1219-1255. (doi: 10.1016/j.aim.2018.10.024)
Brown, K. A. and Zhang, J. J. (2018) Unimodular graded Poisson Hopf algebras. Bulletin of the London Mathematical Society, 50(5), pp. 887-898. (doi: 10.1112/blms.12194)
Brown, K. A. and Macleod, M. J. (2017) The Cohen Macaulay property for noncommutative rings. Algebras and Representation Theory, 20(6), pp. 1433-1465. (doi: 10.1007/s10468-017-9694-z)
Brown, K.A. , O'Hagan, S., Zhang, J.J. and Zhuang, G. (2015) Connected Hopf algebras and iterated Ore extensions. Journal of Pure and Applied Algebra, 219, pp. 2405-2443. (doi: 10.1016/j.jpaa.2014.09.007)
Brown, K. and Gilmartin, P. (2015) Quantum homogeneous spaces of connected Hopf algebras. Journal of Algebra, 454, pp. 400-432.
Brown, K. and Gilmartin, P. (2014) Hopf algebras under finiteness conditions. Palestine Journal of Mathematics, 3(S1), pp. 356-365.
Brown, K. and Macauley, M. (2013) Ambiskew Hopf algebras. Journal of Pure and Applied Algebra, 217(1), pp. 59-74. (doi: 10.1016/j.jpaa.2012.04.007)
Brown, K.A. and Changtong, K. (2010) Symplectic reflection algebras in positive characteristic. Proceedings of the Edinburgh Mathematical Society, 53(1), pp. 61-81. (doi: 10.1017/S0013091507001435)
Brown, K. A. and Zhang, J. J. (2010) Prime regular Hopf algebras of GK-dimension one. Proceedings of the London Mathematical Society, 101(1), pp. 260-302. (doi: 10.1112/plms/pdp060)
Brown, K.A. and Zhang, J.J. (2008) Dualising complexes and twisted Hochschild (co)homology for noetherian Hopf algebras. Journal of Algebra, 320(5), pp. 1814-1850. (doi: 10.1016/j.jalgebra.2007.03.050)
Brown, K.A., Gordon, I.G. and Stroppel, C. (2008) Cherednik, Hecke and quantum algebras as free Frobenius and Calabi–Yau extensions. Journal of Algebra, 319(3), pp. 1007-1034. (doi: 10.1016/j.jalgebra.2007.10.026)
Ardakov, K. and Brown, K.A. (2007) Primeness, semiprimeness and localisation in Iwasawa algebras. Transactions of the American Mathematical Society, 359, pp. 1499-1515. (doi: 10.1090/S0002-9947-06-04153-5)
Brown, K.A., Goodearl, K.R. and Yakimov, M. (2006) Poisson structures on affine spaces and flag varieties. I. Matrix affine Poisson space. Advances in Mathematics, 206(2), pp. 567-629. (doi: 10.1016/j.aim.2005.10.004)
Brown, K. (2005) Unruffled extensions and flatness over central subalgebras. Journal of Algebra, 284, pp. 771-800. (doi: 10.1016/j.jalgebra.2004.10.008)
Brown, K. (2003) Symplectic reflection algebras. Bulletin of the Irish Mathematical Society, 50, pp. 27-49.
Brown, K. and Gordon, I. (2003) Poisson orders, symplectic reflection algebras and representation theory. Journal für die reine und angewandte Mathematik (Crelles Journal), 559, pp. 193-216.
Brown, K. and Gordon, I. (2002) The ramifications of the centres: Quantised function algebras at roots of unity. Proceedings of the London Mathematical Society, 84, pp. 147-178.
Brown, K. and Gordon, I. (2001) The ramification of centres: Lie algebras in positive characteristic and quantised enveloping algebras. Mathematische Zeitschrift, 238, pp. 733-779.
Books
Brown, K.A. and Goodearl, K.R. (2002) Lectures on Algebraic Quantum Groups. Series: Advanced courses in mathematics, CRM Barcelona. Birkhäuser: Basel, Switzerland. ISBN 9783764367145
Book Sections
Brown, K. A. and Goodearl, K. R. (2015) Zariski topologies on stratified spectra of quantum algebras. In: Eisenbud, David (ed.) Commutative Algebra and Noncommutative Algebraic Geometry. Series: Mathematical sciences research institute publications, 68 (68). Cambridge University Press, pp. 63-91. ISBN 9781107149724
Ardakov, K. and Brown, K.A. (2006) Ring-theoretic properties of Iwasawa algebras: a survey. In: Fesenko, I. (ed.) A Collection of Manuscripts Written in Honour of John H. Coates on the Occasion of his Sixtieth Birthday. Series: Documenta mathematica: extra volume (4). Deutsche Mathematiker-Vereinigung: Bielefeld, Germany, pp. 7-33. ISBN 9783936609288
Conference Proceedings
Brown, K. (2007) Noetherian Hopf algebras. In: Antalya Algebra Days, Antalya, Turkey, 22-27 May 2007,