'...the reader obtains the impression that there remains much to discover in commutation theory, and this monograph provides both motivation and a guide to the current state of knowledge.' Mathematical Reviews (1986)

• I: Some Main Results on Commutator Identities.- 1. Introduction and Survey.- 2. The Finite-Dimensional Commutation Condition.- II: Commutation Relations and Regularity Properties for Operators in the Enveloping Algebra of Representations of Lie Groups.- 3. Domain Regularity and Semigroup Commutation Relations.- 4. Invariant-Domain Commutation Theory applied to the Mass-Splitting Principle.- III: Conditions for a System of Unbounded Operators to Satisfy a given Commutation Relation.- 5. Graph-Density applied to Resolvent Commutation, and Operational Calculus.- 6. Graph-Density Applied to Semigroup Commutation Relations.- 7. Construction of Globally Semigroup-invariant C?-domains.- IV: Conditions for a Lie Algebra of Unbounded Operators to Generate a Strongly Continuous Representation of the Lie Group.- 8. Integration of Smooth Operator Lie Algebras.- 9. Exponentiation and Bounded Perturbation of Operator Lie Algebras.- Appendix to Part IV.- V: Lie Algebras of Vector Fields on Manifolds.- 10. Applications of Commutation Theory to Vector-Field Lie Algebras and Sub- Laplacians on Manifolds.- VI: Derivations on Modules of Unbounded Operators with Applications to Partial Differential Operators on Riemann Surfaces.- 11. Rigorous Analysis of Some Commutator Identities for Physical Observables.- Appendix to Part VI.- VII: Lie Algebras of Unbounded Operators: Perturbation Theory, and Analytic Continuation of s?(2, ?)-Modules.- 12. Exponentiation and Analytic Continuation of Heisenberg-Matrix Representations for s?(2, ?).- Appendix to Part VII.- General Appendices.- Appendix A. The Product Rule for Differentiable Operator Valued Mappings.- Appendix B. A Review of Semigroup Folklore, and Integration in Locally Convex Spaces.- Appendix C. The Square of an InfinitesimalGroup Generator.- Appendix E. Compact Perturbations of Semigroups.- Appendix G. Bounded Elements in Operator Lie Algebras.- References.- References to Ouotations.- List of Symbols.

'...the reader obtains the impression that there remains much to discover in commutation theory, and this monograph provides both motivation and a guide to the current state of knowledge.' Mathematical Reviews (1986)

• I: Some Main Results on Commutator Identities.- 1. Introduction and Survey.- 2. The Finite-Dimensional Commutation Condition.- II: Commutation Relations and Regularity Properties for Operators in the Enveloping Algebra of Representations of Lie Groups.- 3. Domain Regularity and Semigroup Commutation Relations.- 4. Invariant-Domain Commutation Theory applied to the Mass-Splitting Principle.- III: Conditions for a System of Unbounded Operators to Satisfy a given Commutation Relation.- 5. Graph-Density applied to Resolvent Commutation, and Operational Calculus.- 6. Graph-Density Applied to Semigroup Commutation Relations.- 7. Construction of Globally Semigroup-invariant C?-domains.- IV: Conditions for a Lie Algebra of Unbounded Operators to Generate a Strongly Continuous Representation of the Lie Group.- 8. Integration of Smooth Operator Lie Algebras.- 9. Exponentiation and Bounded Perturbation of Operator Lie Algebras.- Appendix to Part IV.- V: Lie Algebras of Vector Fields on Manifolds.- 10. Applications of Commutation Theory to Vector-Field Lie Algebras and Sub- Laplacians on Manifolds.- VI: Derivations on Modules of Unbounded Operators with Applications to Partial Differential Operators on Riemann Surfaces.- 11. Rigorous Analysis of Some Commutator Identities for Physical Observables.- Appendix to Part VI.- VII: Lie Algebras of Unbounded Operators: Perturbation Theory, and Analytic Continuation of s?(2, ?)-Modules.- 12. Exponentiation and Analytic Continuation of Heisenberg-Matrix Representations for s?(2, ?).- Appendix to Part VII.- General Appendices.- Appendix A. The Product Rule for Differentiable Operator Valued Mappings.- Appendix B. A Review of Semigroup Folklore, and Integration in Locally Convex Spaces.- Appendix C. The Square of an InfinitesimalGroup Generator.- Appendix E. Compact Perturbations of Semigroups.- Appendix G. Bounded Elements in Operator Lie Algebras.- References.- References to Ouotations.- List of Symbols.