Quantum Algebras

Book

Lectures on Algebraic Quantum Groups (with K.A. Brown)

Advanced Courses in Mathematics CRM Barcelona

Basel (2002) Birkhäuser

Math. Reviews 03f:16067; Zentralblatt 1027.17010

Proc. Edinburgh Math. Soc. 48 (2005) 507-8

Expository and Overview Articles

Spectra of quantum algebras

in Recent Advances in Noncommutative Algebra and Geometry (K.A, Brown, T.J. Hodges, M. Vancliff, J.J. Zhang, eds.)

Contemp. Math. 801 (2024) 95-109

Math. Reviews MR4756379

Quantum cluster algebras and quantum nilpotent algebras (with M.T. Yakimov)

Proc. Nat. Acad. Sci. USA 111 (2014) 9696-9703

Math. Reviews MR3263301; Zentralblatt 1355.16037

Semiclassical limits of quantized coordinate rings

in Advances in Ring Theory (D.V. Huynh and S. Lopez-Permouth, Eds.), Basel (2009) Birkhäuser, pp. 165-204

Math. Reviews 11h:20107; Zentralblatt 1202.16027

Quantized coordinate rings and related noetherian algebras

in Proc. 35th. Symposium on Ring Theory and Representation Theory (Okayama 2002) (Y. Hirano, Ed.), Okayama (2003) Univ. of Okayama, pp. 19-45

Quantized primitive ideal spaces as quotients of affine algebraic varieties

in Quantum Groups and Lie Theory (Durham 1999) (A. Pressley, Ed.), London Math. Soc. Lecture Notes 290, Cambridge (2001) Cambridge Univ. Press, pp. 130-148

Math. Reviews 03f:16068; Zentralblatt 1042.16032

Prime spectra of quantized coordinate rings

in Interactions between Ring Theory and Representations of Algebras (Murcia, 1998) (F. Van Oystaeyen and M. Saorin, Eds.), New York (2000) Dekker, pp. 205-237

Math. Reviews 01b:16052; Zentralblatt 984.16039

Research Articles

Binomial ideals in quantum tori and quantum affine spaces

J. Algebra 657 (2024), 638-674

Math. Reviews MR4758301

Spectra of quantum algebras

in Recent Advances in Noncommutative Algebra and Geometry (K.A, Brown, T.J. Hodges, M. Vancliff, J.J. Zhang, eds.)

Contemp. Math. 801 (2024) 95-109

Math. Reviews MR4756379

Cluster algebra structures on Poisson nilpotent algebras (with M.T. Yakimov)

Memoirs Amer. Math. Soc. No. 1445 (2023), v+100pp.

Math. Reviews MR4664284; Zentralblatt 1535.13001

Poisson catenarity in Poisson nilpotent algebras (with S. Launois)

J. Algebra 611 (2022) 265-284

Math. Reviews MR4474637; Zentralblatt 1521.17045

Integral quantum cluster structures (with M.T. Yakimov)

Duke Math. J. 170 (2021) 1137-1200

Math. Reviews MR4255051; Zentralblatt 1478.13036

Catenarity in quantum nilpotent algebras (with S. Launois)

Proc. Amer. Math. Soc. Ser. B 7 (2020) 202--214

Math. Reviews MR4188200; Zentralblatt 1469.16070

The Berenstein-Zelevinsky quantum cluster algebra conjecture (with M.T. Yakimov)

J. European Math. Soc. 22 (2020) 2453-2509

Math. Reviews MR4118613; Zentralblatt 1471.13046

Tauvel's height formula for quantum nilpotent algebras (with T.H. Lenagan and S. Launois)

Communic. in Algebra 47 (2019) 4194-4209

Math. Reviews MR3975998; Zentralblatt 1478.16025

Quantum cluster algebra structures on quantum nilpotent algebras (with M.T. Yakimov)

Memoirs Amer. Math. Soc. No. 1169 (2017) v+119 pp.

Zentralblatt 1372.16040; Math Reviews MR3633289

From quantum Ore extensions to quantum tori via noncommutative UFDs (with M.T. Yakimov)

Advances in Math. 300 (2016) 672-716

Zentralblatt 1352.16037; Math Reviews MR3534843

The isomorphism problem for multiparameter quantized Weyl algebras (with J.T. Hartwig)

Sao Paolo J. Math. Sci. 9 (2015) 53-61

Zentralblatt 1332.16027; Math Reviews MR3413379

Unipotent and Nakayama automorphisms of quantum nilpotent algebras (with M.T. Yakimov)

in Commutative Algebra and Noncommutative Algebraic Geometry (II) (D. Eisenbud, et al., eds.)

MSRI Publ. 68

Cambridge (2015) Cambridge University Press, pp. 181-212

Zentralblatt 1359.16036; Math Reviews MR3496865

Zariski topologies on stratified spectra of quantum algebras (with K.A. Brown)

in Commutative Algebra and Noncommutative Algebraic Geometry (II) (D. Eisenbud, et al., eds.)

MSRI Publ. 68

Cambridge (2015) Cambridge University Press, pp. 63-91

Zentralblatt 1359.16035; Math Reviews MR3496861

Quantum cluster algebras and quantum nilpotent algebras (with M.T. Yakimov)

Proc. Nat. Acad. Sci. USA 111 (2014) 9696-9703

Math. Reviews 3263301; Zentralblatt 1355.16037

Primitive ideals in quantum SL₃ and GL₃ (with T. H. Lenagan)

in New Trends in Noncommutative Algebra (Seattle 2010) (P. Ara, et al., eds.)

Contemp. Math. 562 (2012) 115-140

Math. Reviews MR2905557; Zentralblatt 1264.16036

Torus-invariant prime ideals in quantum matrices, totally nonnegative cells and symplectic leaves (with S. Launois and T.H. Lenagan)

Math. Zeitschrift 269 (2011) 29-45

Math. Reviews 12h:16071; Zentralblatt 1234.16018

Totally nonnegative cells and matrix Poisson varieties (with S. Launois and T.H. Lenagan)

Advances in Math. 226 (2011) 779-826

Math. Reviews 12e:53162; Zentralblatt 1210.14055

The Dixmier-Moeglin equivalence and a Gel'fand-Kirillov problem for Poisson polynomial algebras (with S. Launois)

Bull. Soc. Math. France 139 (2011) 1-39

Math. Reviews 12e:17045; Zentralblatt 1226.17016

Semiclassical limits of quantized coordinate rings

in Advances in Ring Theory (D.V. Huynh and S. Lopez-Permouth, Eds.), Basel (2009) Birkhäuser, pp. 165-204

Math. Reviews 11h:20107; Zentralblatt 1202.16027

Semiclassical limits of quantum affine spaces (with E.S. Letzter)

Proc. Edinburgh Math. Soc. 52 (2009) 387-407

Zentralblatt 1184.16037; Math. Reviews 10h:17026

Poisson structures on affine spaces and flag varieties. II. (with M. Yakimov)

Trans. Amer. Math. Soc. 361 (2009) 5753-5780

Math. Reviews 10k:14092; Zentralblatt 1179.53087

Homological properties of quantized coordinate rings of semisimple groups (with J. J. Zhang)

Proc. London Math. Soc. (3) 94 (2007) 647-671

Math. Reviews 08e:20077; Zentralblatt 1120.16039

A Dixmier-Moeglin equivalence for Poisson algebras with torus actions

in Algebra and Its Applications (D. V. Huynh, S. K. Jain, and S. R. Lopez-Permouth, Eds.), Contemp. Math. 419 (2006) 131-154

Math. Reviews 08a:17024; Zentralblatt 1147.17017

Commutation relations for arbitrary quantum minors

Pacific J. Math. 228 (2006) 63-102

Math. Reviews 07j:17019; Zentralblatt 1125.16034

Poisson structures on affine spaces and flag varieties. I. Matrix affine Poisson space (with K. A. Brown and M. Yakimov)

Advances in Math. 206 (2006) 567-629

Math. Reviews 07k:14094; Zentralblatt 1105.53062

Quantized coinvariants at transcendental q (with T.H. Lenagan)

in Hopf Algebras in Noncommutative Geometry and Physics (Brussels, 2002) (S. Caenepeel and F. Van Oystaeyen, Eds.), pp. 155-165

New York (2005) Dekker

Math. Reviews 05j:20061; Zentralblatt 1083.16024

Winding-invariant prime ideals in quantum 3x3 matrices (with T.H. Lenagan)

J. Algebra 260 (2003) 657-687

Math. Reviews 04g:20069; Zentralblatt 1059.16035

Prime ideals invariant under winding automorphisms in quantum matrices (with T.H. Lenagan)

Internat. J. Math. 13 (2002) 497-532

Math. Reviews 03h:20091; Zentralblatt 1054.16030

Quantized primitive ideal spaces as quotients of affine algebraic varieties

in Quantum Groups and Lie Theory (Durham 1999) (A. Pressley, Ed.), London Math. Soc. Lecture Notes 290, Cambridge (2001) Cambridge Univ. Press, pp. 130-148

Math. Reviews 03f:16068; Zentralblatt 1042.16032

Quantum n-space as a quotient of classical n-space (with E.S. Letzter)

Trans. Amer. Math. Soc. 352 (2000) 5855-5876

Math. Reviews 01e:16061; Zentralblatt 978.16041

The first fundamental theorem of coinvariant theory for the quantum general linear group (with T.H. Lenagan and L. Rigal)

Publ. Research Inst. Math. Sci. Kyoto 36 (2000) 269-296

Math. Reviews 01k:20112; Zentralblatt 972.16022

Prime ideals in certain quantum determinantal rings (with T.H. Lenagan)

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

Math. Reviews 01k:16081; Zentralblatt 982.16020

Prime spectra of quantized coordinate rings

in Interactions between Ring Theory and Representations of Algebras (Murcia, 1998) (F. Van Oystaeyen and M. Saorin, Eds.), New York (2000) Dekker, pp. 205-237

Math. Reviews 01b:16052; Zentralblatt 984.16039

Quantum determinantal ideals (with T.H. Lenagan)

Duke Math. J. 103 (2000) 165-190

Math. Reviews 01k:16080; Zentralblatt 958.16025

The Dixmier-Moeglin equivalence in quantum coordinate rings and quantized Weyl algebras (with E.S. Letzter)

Trans. Amer. Math. Soc. 352 (2000) 1381-1403

Math. Reviews 00j:16040; Zentralblatt 978.16040

Prime and primitive spectra of multiparameter quantum affine spaces (with E.S. Letzter)

in Trends in Ring Theory. Proc. Miskolc Conf. 1996 (V. Dlab and L. Marki, Eds.)

Canad. Math. Conf. Proc. Series 22 (1998) 39-58

Math. Reviews 99h:16045; Zentralblatt 904.16001

Homological aspects of noetherian P.I. Hopf algebras, and irreducible modules of maximal dimension (with K.A. Brown)

J. Algebra 198 (1997) 240-265

Math. Reviews 99c:16036; Zentralblatt 892.16022

A Hilbert basis theorem for quantum groups (with K.A. Brown)

Bull. London Math. Soc. 29 (2) (1997) 150-158

Math. Reviews 97m:16068; Zentralblatt 888.17003

Prime spectra of quantum semisimple groups (with K.A. Brown)

Trans. Amer. Math. Soc. 348 (1996) 2465-2502

Math. Reviews 96i:17007; Zentralblatt 857.16026

Catenarity in quantum algebras (with T.H. Lenagan)

J. Pure Appl. Algebra 111 (1996) 123-142

Math. Reviews 97e:16054; Zentralblatt 864.16018

Prime factor algebras of the coordinate ring of quantum matrices (with E.S. Letzter)

Proc. Amer. Math. Soc. 121 (1994) 1017-1025

Math. Reviews 94j:16066; Zentralblatt 812 (1995) 16039

Prime ideals in skew and q-skew polynomial rings (with E.S. Letzter)

Memoirs Amer. Math. Soc. No. 521 (1994)

Math. Reviews 94j:16051; Zentralblatt 814 (1995) 16026

Prime ideals in skew polynomial rings and quantized Weyl algebras

J. Algebra 150 (1992) 324-377

Math. Reviews 93h:16051; Zentralblatt 779.16010