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

Quantum cluster algebras and quantum nilpotent algebras (with M.T. Yakimov)
Proc. Nat. Acad. Sci. USA 111 (2014) 9696-9703.
Math. Reviews 3263301
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

The isomorphism problem for multiparameter quantized Weyl algebras (with J.T. Hartwig)
Sao Paolo J. Math. Sci. 9 (2015) 53-61
Unipotent and Nakayama automorphisms of quantum nilpotent algebras (with M.T. Yakimov)
in Commutative Algebra and Noncommutative Algebraic Geometry (II) (J.T. Stafford, et al., eds.)
MSRI Publ. 68 (2015)
Zariski topologies on stratified spectra of quantum algebras (with K.A. Brown)
in Commutative Algebra and Noncommutative Algebraic Geometry (II) (J.T. Stafford, et al., eds.)
MSRI Publ. 68 (2015)
Quantum cluster algebra structures on quantum nilpotent algebras (with M.T. Yakimov)
Memoirs Amer. Math. Soc.
From quantum Ore extensions to quantum tori via noncommutative UFDs (with M.T. Yakimov)
Advances in Math.
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 2905557; 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

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goodearl@math.ucsb.edu

Last Modified: August 2015

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