New Trends in Noncommutative Algebra.

Intro -- 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 ℋ-strata with respect to dimension -- 4. The proportion of primitive ℋ-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 (ℓ,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 ₃ and ₃ -- 0. Introduction -- 1. Background and notation -- 2. Torus-invariant prime ideals -- 3. Localizations -- 4. Centers of localizations -- 5. Primitive ideals -- 6. General consequences -- 7. Appendix. Homological conditions -- References -- Irreducible components of module varieties: projective equations and rationality -- 1. Introduction and conventions -- 2. Prerequisites concerning the affine and projective module varieties -- 3. Transfer of properties from the ( ) to the larger parametrizing varieties -- 4. The varieties ( ) -- 5. Carlson's Example revisited and generalized -- 6. Projective equations -- References -- Poisson brackets and Poisson spectra in polynomial algebras -- 1. Introduction -- 2. Poisson triples on -- 3. Poisson brackets for exact and -exact brackets -- 4. Examples -- References -- Hopf Action on Calabi-Yau algebras -- Introduction -- 1. Preliminaries -- 2. Calabi-Yau properties of the smash product -- 3. Superpotentials of # -- References -- Finitely generated, non-artinian monolithic modules -- 1. Introduction -- 2. The construction. -- 3. Examples (B.1)-(B.3). -- 4. Down-up Algebras. -- 5. Remarks and Problems. -- References.

Regular algebras of dimension 4 with 3 generators -- 0. Introduction -- 1. Preliminaries -- 2. Beginning analysis of ℤ^{×2}-graded AS-regular algebras -- 3. Classification of ℤ^{×2}-graded AS-regular algebras with 3 generators -- 4. Proof of the main results -- 5. Graded isomorphisms and automorphisms -- Acknowledgments -- References -- Galois invariants of ₁-groups of Iwasawa algebras. -- Introduction -- 1. The case of "local" and "number" fields -- 2. The case of rings of integers of "local" fields -- 3. The case of residue class fields -- References -- Strata of prime ideals of De Concini-Kac-Procesi algebras and Poisson geometry -- 1. Introduction -- 2. Quantized nilpotent algebras -- 3. Poisson structures on flag varieties -- 4. Dimensions of the Goodearl-Letzter strata -- Acknowledgements -- References -- Twisted Deformation Quantization of Algebraic Varieties (Survey) -- 0. Introduction -- 1. Some background on Deformation Quantization -- 2. Poisson Deformations of Algebraic Varieties -- 3. Associative Deformations of Algebraic Varieties -- 4. Deformation Quantization -- 5. Twisted Deformations of Algebraic Varieties -- 6. Twisted Deformation Quantization -- Appendix A. DG Lie Algebras and Deformations -- Appendix B. The Universal Quantization Map -- Appendix C. The _{∞} quasi-isomorphism on the Level of Sheaves -- Appendix D. Twisted Deformations and their Gauge Gerbes -- References.

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