Algorithmic methods in non-commutative algebra : applications to quantum groups / by José Bueso, José Gómez-Torrecillas, and Alain Verschoren.

Format:

Book

Author/Creator:

Bueso, J. L. (José Luis), 1949-

Contributor:

Gómez-Torrecillas, José.

Verschoren, A., 1954-

Rosengarten Family Fund.

Series:

Mathematical modelling--theory and applications ; v. 17.

Mathematical modelling--theory and applications ; v. 17

Language:

English

Subjects (All):

Noncommutative algebras.

Algorithms.

Quantum groups.

Physical Description:

xi, 298 pages ; 25 cm.

Place of Publication:

Dordrecht ; Boston : Kluwer Academic Publishers, [2003]

Contents:

Chapter 1. Generalities on rings 1

1. Rings and ideals 2

2. Modules and chain conditions 13

3. Ore extensions 20

4. Factorization 28

6. Quantum groups 48

Chapter 2. Grobner basis computation algorithms 63

1. Admissible orders 63

2. Left Poincare-Birkhoff-Witt Rings 68

4. The Division Algorithm 77

5. Grobner bases for left ideals 80

6. Buchberger's Algorithm 84

7. Reduced Grobner Bases 94

8. Poincare-Birkhoff-Witt rings 97

9. Effective computations for two-sided ideals 101

Chapter 3. Poincare-Birkhoff-Witt Algebras 109

1. Bounding quantum relations 109

2. Misordering 114

3. The Diamond Lemma 116

4. Poincare-Birkhoff-Witt Theorems 123

6. Iterated Ore Extensions 130

Chapter 4. First applications 137

1. Applications to left ideals 137

2. Cyclic finite-dimensional modules 143

3. Elimination 145

4. Graded and filtered algebras 150

5. The [omega]-filtration of a PBW algebra 153

6. Homogeneous Grobner bases 155

7. Homogenization 162

Chapter 5. Grobner bases for modules 169

1. Grobner bases and syzygies 169

2. Computation of the syzygy module 171

3. Admissible orders in stable subsets 175

4. Grobner bases for modules 177

5. Grobner bases for subbimodules 185

6. Elementary applications of Grobner bases for modules 188

7. Graded and filtered modules 192

8. The [omega]-filtration of a module 194

9. Homogeneous Grobner bases 196

10. Homogenization 197

Chapter 6. Syzygies and applications 203

1. Syzygies for modules 203

2. Intersections 209

3. Applications to finitely presented modules 214

4. Schreyer's order 217

5. Free resolutions 219

6. Computation of Hom and Ext. 223

Chapter 7. The Gelfand-Kirillov dimension and the Hilbert polynomial 239

1. The Gelfand-Kirillov dimension 239

2. The Hilbert function of a stable subset 246

3. The Hilbert function of a module over a PBW algebra 253

4. The Gelfand-Kirillov dimension of PBW algebras 255

Chapter 8. Primality 263

1. Localization 263

2. The Ore condition and syzygies 275

3. A primality test 276

4. The primality test in iterated differential operator rings 282

5. The primality test in coordinate rings of quantum spaces 283.

Notes:

Includes bibliographical references (pages 293-298) and index.

Local Notes:

Acquired for the Penn Libraries with assistance from the Rosengarten Family Fund.

ISBN:

1402014023

OCLC:

52216256