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

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

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

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

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

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

Commutation relations for arbitrary quantum minors

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

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

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