Contributions to Algebra : A Collection of Papers Dedicated to Ellis Kolchin.

Front Cover -- Contributions to Algebra: A Collection of Papers Dedicated to Ellis Kolchin -- Copyright Page -- Table of Contents -- Dedication -- List of contributors -- Preface -- Chapter 1. Quadratic modules over polynomial rings -- Introduction -- 1. Definitions, and background of the problem -- 2. Reduction by the Cancellation Theorem to low ranks -- 3. Quadratic spaces of low rank -- 4. Proof of the Cancellation Theorem -- 5. Proof of Karoubi's theorem -- References -- Chapter 2. The action of the universal modular group on certain boundary points -- Text -- References -- Chapter 3. Differentially closed fields: a model-theoretic tour -- Introduction -- 1. Background -- 2. Model completions -- 3. Main results -- 4. Some properties of differential closures and some immediate consequences -- 5. Notes -- Appendix: Details of uniqueness proof filled in Definitions -- References -- Chapter 4. On finite projective groups -- 1. Introduction -- 2. Preliminaries -- 3. Finite strongly irreducible linear groups -- 4. Case I -- 5. Case II -- 6. Quasi-primitive linear groups -- References -- Chapter 5. Unipotent differential algebraic groups -- Introduction of subject matter and notation -- 1. The structure of unipotent differential algebraic groups -- 2. Commutative linear unipotent differential algebraic groups -- 3. Differential rational cohomology -- 4. Extensions of differential algebraic groups -- 5. The groupsH∆2(Ga, Ga) and Cent Ext∆(Ga, Ga) -- References -- Chapter 6. Solutions in the general solution -- 1. Introduction -- 2. Differentially closed places -- 3. Preliminary criteria -- 4. Algebraic extensions -- 5. Final criteria -- 6. Several indeterminates -- References -- Chapter 7. Folk theorems on elliptic equations -- Text -- References -- Chapter 8. Limit properties of stochastic matrices -- 1. Preliminaries -- 2. Shrinking matrices.

3. Analysis of supports -- 4. The case d = 1 -- 5. The general case -- Chapter 9. A fixed-point characterization of linearly reductive groups -- 1. Introduction -- 2. Proof of the theorem -- References -- Chapter 10. Orthogonal and unitary invariants of families of subspaces -- 1. Pairs of subspaces -- 2. Systems of lines -- 3. Representations of H*-algebras -- 4. Systems of subspaces -- References -- Chapter 11. The Macdonald-Kac formulas as a consequence of the Euler-Poincaré principle -- Introduction -- 1. The Lie algebras of Kac and Moody -- 2. Quasisimple modules -- 3. Homology associated with F-parabolic subalgebras -- 4. Combinatorial identities -- References -- Chapter 12. The characters of reductive p-adic groups -- Text -- References -- Chapter 13. Basic constructions in group extension theory -- 1. Introduction -- 2. Preliminaries -- 3. Group extensions -- 4. Crossed homomorphisms -- 5. Transgression -- 6. Inflation -- 7. Abelian kernels -- 8. Cohomology -- Chapter 14. On the hyperalgebra of a semisimple algebraic group -- 1. The hyperalgebra -- 2. The algebra ur and its representations -- 3. Tensor products -- 4. Completely reducible G-modules -- 5. Mumford's conjecture -- References -- Chapter 15. A notion of regularity for differential local algebras -- Introduction -- 1. Some preliminary facts about Kähler differentials -- 2. Regular differential algebras -- 3. A sufficient condition for regularity -- 4. Regular graded modules -- 5. The openness of the set of regular points -- 6. Regularity for Δ-fields -- References -- Chapter 16. The Engel-Kolchin theorem revisited -- 1. Introduction -- 2. A second unification of Kolchin's theorem and Levitzki's theorem -- 3. Two more theorems -- 4. Lie and Jordan analogues -- 5. The infinite case -- References -- Chapter 17. Prime differential ideals in differential rings.

1. Special differential rings -- 2. The prime differential spectrum of a differential ring -- References -- Chapter 18. Constrained cohomology -- Introduction -- 1. Constrained cohomology groups -- 2. Galois cohomology -- 3. Change of group -- 4. F-Cohomology -- 5. Change of field -- 6. The Hochschild-Serre sequence -- References -- Chapter 19. The integrability condition of deformations of CR structures -- Introduction -- 1. The integrability condition of CR structures -- 2. The integrability condition of deformations -- References -- Chapter 20. Noetherian rings with many derivations -- Text -- References -- Chapter 21. Hopf maps and quadratic forms over Z -- 1. Hurwitz triple and the map f -- 2. The map f and the map h -- 3. The family £ -- 4. Hopf fibration S15 → S8 over Z -- References -- Chapter 22. Families of subgroup schemes of formal groups -- 1. Strict families of finite subgroup schemes of formal groups -- 2. Liftability of abelian varieties -- References -- Chapter 23. An effective lower bound on the "diophantine" approximation of algebraic functions by rational functions (II) -- Text -- References -- Chapter 24. On elementary, generalized elementary, and liouvillian extension fields -- Text -- References -- Chapter 25. Derivations and valuation rings -- Text -- References -- Chapter 26. On theorems of Lie-Kolchin, Borel, and Lang -- Text -- References -- Chapter 27. A differential-algebraic study of the intrusion of logarithms into asymptotic expansions -- A. Introduction -- B. Some basic notations, procedures, and lemmas for the adjunction rank-rise problem -- C. Instability ladders for differential polynomials of Class(V, r) -- D. Instability ladders for r-normal differential polynomials -- E. Instability ladders for asymptotically nonsingular differential polynomials -- F. Rank-rise results for the general first-order equation.

G. Other rank-rise results [Note 23] -- Appendix -- References -- Chapter 28. A "theorem of Lie-Kolchin" for trees -- Introduction -- 1. Trees -- 2. Various fixed-point properties -- 3. Solvable groups -- 4. Algebraic simple groups of relative rank ≥ 2 -- 5. The rank 1 case -- References -- Chapter 29. Regular elements in anisotropic tori -- Introduction -- 1. -- 2. -- 3. Classical groups -- 4. Anisotropic tori in classical groups -- 5. Results for the classical groups -- 6. Type 1Al -- 7. Type1Bl -- 8. Type 1Cl -- 9. Type 1Dl -- 10. Type 2Al -- 11. Type 2Dl -- 12. The Suzuki groups 2C2(q2) -- 13. Groups of type 3D4 -- 14. Conjugacy classes in the Weyl group of F4 -- 15. Groups of type 1F4 -- 16. The Ree groups 2F4 -- 17. Groups of type 1G2 -- 18. Groups of type 2G2 -- 19. Endomorphisms σ with cyclic centralizer in W -- 20. Groups of type 1E6 -- 21. Groups of type 2E6 -- 22. Groups of type 1E7 -- 23. Groups of type 1E8 -- References.

Description based on publisher supplied metadata and other sources.

Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.