New trends in noncommutative algebra : conference in honor of Ken Goodearl's 65th birthday, August 9-14, 2010, University of Washington, Seattle, Washington

Noncommutative algebras
American Mathematical Society
2012
EISBN 0821884972
Preface.
Ken Goodearl's contributions to ring theory.
1. C*-algebras and von Neumann regular rings.
2. Differential operator rings..
3. Skew and -skew polynomial rings. Quantum coordinate rings..
4. Stratification..
5. H-prime ideals, totally nonnegative grassmanians, and symplectic leaves in matrix Poisson varieties..
6. Homological aspects of quantum groups and noetherian Hopf algebras..
7. Gems off the path..
8. Expository works..
Bibliography.
Row-finite equivalents exist only for row-countable graphs.
References.
The controller subgroup of one-sided ideals in completed group rings.
1. Introduction.
2. The controller subgroup for profinite groups.
3. Compact -adic analytic groups.
References.
Enumeration of torus-invariant strata with respect to dimension in the big cell of the quantum minuscule Grassmannian of type _{ }.
1. Introduction.
2. Cauchon diagrams and Permutations in type _{ }.
3. Enumeration of a-strata with respect to dimension.
4. The proportion of primitive a-primes.
References.
Primitive algebraic algebras of polynomially bounded growth.
1. Introduction.
2. Gelfand-Kirillov dimension.
3. Affinization.
4. Algebraic algebras.
5. Affinization with two generators.
6. Questions.
Acknowledgments.
References.
Conic bundles and Clifford algebras.
1. Introduction.
2. Quadratic Forms over Schemes and Associated Conic Bundles.
3. Even Clifford Algebras.
4. Quaternion Algebras.
5. Brauer-Severi Varieties of Even Clifford Algebras.
6. Quaternion algebras of conic bundles.
7. Chern classes and - ³.
8. Del Pezzo Orders and Conic Bundles.
References.
Cell modules and canonical basic sets for Hecke algebras from Cherednik algebras.
1. Introduction.
2. Hecke and Cherednik algebras.
3. Category and basic sets.
4. Forms and Standard Modules.
5. Type (â„“,1, ).
References.
On representations of Clifford algebras of Ternary cubic forms.
1. Introduction.
2. Generalities on Representations of Generalized Clifford Algebras and Ulrich Bundles.
3. The Case of Ternary Cubic Forms.
References.
Certain subgroups of Weyl groups are split.
1. Introduction.
2. Symmetric groups.
3. Direct products.
4. Wreath products.
5. Division algebras.
6. Schur indices.
7. Classical Weyl groups.
8. Exceptional Weyl groups.
9. Positive characteristic.
10. Real reflection groups.
11. Open questions.
References.
Primitive ideals in quantum a and a.
0. Introduction.
1. Background and notation.
2. Torus-invariant prime ideals.
3. Localizations.
4. Centers of localizations.
5. Primitive ideals.
6. General consequences.
7. A --endix. Homological conditions.
References .
Irreducible components of module varieties: projective equations and rationality.
Poisson brackets and Poisson spectra in polynomial algebras.
Hopf Action on Calabi-Yau algebras.
Finitely generated, non-artinian monolithic modules.
Regular algebras of dimension 4 with 3 generators .
Galois invariants of x-groups of Iwasawa algebras.
Strata of prime ideals of De Concini–Kac–Procesi algebras and Poisson geometry --Twisted Deformation Quantization of Algebraic Varieties (Survey).
Ken Goodearl's contributions to ring theory.
1. C*-algebras and von Neumann regular rings.
2. Differential operator rings..
3. Skew and -skew polynomial rings. Quantum coordinate rings..
4. Stratification..
5. H-prime ideals, totally nonnegative grassmanians, and symplectic leaves in matrix Poisson varieties..
6. Homological aspects of quantum groups and noetherian Hopf algebras..
7. Gems off the path..
8. Expository works..
Bibliography.
Row-finite equivalents exist only for row-countable graphs.
References.
The controller subgroup of one-sided ideals in completed group rings.
1. Introduction.
2. The controller subgroup for profinite groups.
3. Compact -adic analytic groups.
References.
Enumeration of torus-invariant strata with respect to dimension in the big cell of the quantum minuscule Grassmannian of type _{ }.
1. Introduction.
2. Cauchon diagrams and Permutations in type _{ }.
3. Enumeration of a-strata with respect to dimension.
4. The proportion of primitive a-primes.
References.
Primitive algebraic algebras of polynomially bounded growth.
1. Introduction.
2. Gelfand-Kirillov dimension.
3. Affinization.
4. Algebraic algebras.
5. Affinization with two generators.
6. Questions.
Acknowledgments.
References.
Conic bundles and Clifford algebras.
1. Introduction.
2. Quadratic Forms over Schemes and Associated Conic Bundles.
3. Even Clifford Algebras.
4. Quaternion Algebras.
5. Brauer-Severi Varieties of Even Clifford Algebras.
6. Quaternion algebras of conic bundles.
7. Chern classes and - ³.
8. Del Pezzo Orders and Conic Bundles.
References.
Cell modules and canonical basic sets for Hecke algebras from Cherednik algebras.
1. Introduction.
2. Hecke and Cherednik algebras.
3. Category and basic sets.
4. Forms and Standard Modules.
5. Type (â„“,1, ).
References.
On representations of Clifford algebras of Ternary cubic forms.
1. Introduction.
2. Generalities on Representations of Generalized Clifford Algebras and Ulrich Bundles.
3. The Case of Ternary Cubic Forms.
References.
Certain subgroups of Weyl groups are split.
1. Introduction.
2. Symmetric groups.
3. Direct products.
4. Wreath products.
5. Division algebras.
6. Schur indices.
7. Classical Weyl groups.
8. Exceptional Weyl groups.
9. Positive characteristic.
10. Real reflection groups.
11. Open questions.
References.
Primitive ideals in quantum a and a.
0. Introduction.
1. Background and notation.
2. Torus-invariant prime ideals.
3. Localizations.
4. Centers of localizations.
5. Primitive ideals.
6. General consequences.
7. A --endix. Homological conditions.
References .
Irreducible components of module varieties: projective equations and rationality.
Poisson brackets and Poisson spectra in polynomial algebras.
Hopf Action on Calabi-Yau algebras.
Finitely generated, non-artinian monolithic modules.
Regular algebras of dimension 4 with 3 generators .
Galois invariants of x-groups of Iwasawa algebras.
Strata of prime ideals of De Concini–Kac–Procesi algebras and Poisson geometry --Twisted Deformation Quantization of Algebraic Varieties (Survey).
