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Preface; Non-Associative and Non-Commutative Algebra and Operator Theory; Contents; Part I Invited Talks; 1 Group Theory and the Capitulation Problem for Some Number Fields; 1.1 Introduction; 1.2 Main Results; 1.2.1 First Case: Cl2(k) is of Type (2, 2); 1.2.2 Second Case: Cl2(k) is of Type (2, 4); 1.2.3 Third Case: Cl2(k) is of Type (2, 2, 2); 1.3 Preliminary Results; 1.4 Proofs of the Main Results; 1.4.1 First Case: Cl2(k) is of Type (2, 2); 1.4.2 Second Case: Cl2(k) is of Type (2, 4); References; 2 On Space-Time Codes Arising from Free Modules and Algebras over an Integral Domain
2.1 Introduction2.2 Free Modules and Free Algebras over an Integral Domain; 2.3 Examples of STBCs Over Integral Domains; 2.3.1 Examples from Extensions of Integral Domains; 2.3.2 Examples from Associative Algebras over Integral Domains; 2.3.3 An Example from Nonassociative Algebras over Integral Domains; References; 3 Graded Modules over Superconformal Algebras; 3.1 Introduction; 3.2 Lie Superconformal Algebras; 3.3 Jordan Superconformal Algebras; 3.4 Locality; 3.5 Graded Modules; References; 4 On Deformations of n-Lie Algebras; 4.1 Introduction
4.2 Definitions and Examples of n-Lie Algebras and Other Types of n-ary Algebras4.2.1 n-Lie Algebras; 4.2.2 n-ary Algebras of Associative Type; 4.2.3 Representations of n-Lie Algebras; 4.2.4 Central Extensions; 4.3 Deformation Cohomology of n-Lie Algebras; 4.4 Formal Deformation of n-Lie Algebras; 4.4.1 One-Parameter Formal Deformation of n-Lie Algebras; 4.4.2 Noncommutative One-Parameter Formal Deformations; 4.5 Global Deformations; 4.6 The Algebraic Varieties Lienm and Degenerations ; 4.7 n-Lie-Poisson Algebras and Quantization; 4.7.1 n-Lie-Poisson Algebras
4.7.2 Quantization of Nambu Mechanics4.7.3 Ternary Virasoro-Witt Algebras; References; 5 Morita Equivalence and Morita Invariant Properties: Applications in the Context of Leavitt Path Algebras; 5.1 Introduction; 5.2 Morita Equivalence for Rings Without a Unit Element: Local Rings at Elements; 5.3 Applications to Morita Invariant Properties; 5.4 Applications in the Context of Leavitt Path Algebras; References; 6 On Commuting U-Operators in Jordan Algebras; 6.1 An Introduction; 6.2 A Counter-Example; 6.3 The Non-degenerate Case; References; Part II Contributed Talks
7 Gradings on Algebras over Algebraically Closed Fields7.1 Introduction; 7.2 Gradings; 7.3 Main Results; References; 8 On the Set of Artinian Subrings of Infinite Products of Rings; 8.1 Introduction; 8.2 Artinian Subrings of an Infinite Product of Rings; 8.3 The Set of Subrings Which Are Directed Unions of Artinian Subrings; References; 9 Noncommutative Gröbner Basis over a Divisible and Annihilable Ring; 9.1 Introduction; 9.2 Preliminaries; 9.2.1 D-A Rings; 9.2.2 Admissible Orderings; 9.3 Non Commutative Gröbner Bases; 9.3.1 Reduction; 9.3.2 A-polynomials
2.1 Introduction2.2 Free Modules and Free Algebras over an Integral Domain; 2.3 Examples of STBCs Over Integral Domains; 2.3.1 Examples from Extensions of Integral Domains; 2.3.2 Examples from Associative Algebras over Integral Domains; 2.3.3 An Example from Nonassociative Algebras over Integral Domains; References; 3 Graded Modules over Superconformal Algebras; 3.1 Introduction; 3.2 Lie Superconformal Algebras; 3.3 Jordan Superconformal Algebras; 3.4 Locality; 3.5 Graded Modules; References; 4 On Deformations of n-Lie Algebras; 4.1 Introduction
4.2 Definitions and Examples of n-Lie Algebras and Other Types of n-ary Algebras4.2.1 n-Lie Algebras; 4.2.2 n-ary Algebras of Associative Type; 4.2.3 Representations of n-Lie Algebras; 4.2.4 Central Extensions; 4.3 Deformation Cohomology of n-Lie Algebras; 4.4 Formal Deformation of n-Lie Algebras; 4.4.1 One-Parameter Formal Deformation of n-Lie Algebras; 4.4.2 Noncommutative One-Parameter Formal Deformations; 4.5 Global Deformations; 4.6 The Algebraic Varieties Lienm and Degenerations ; 4.7 n-Lie-Poisson Algebras and Quantization; 4.7.1 n-Lie-Poisson Algebras
4.7.2 Quantization of Nambu Mechanics4.7.3 Ternary Virasoro-Witt Algebras; References; 5 Morita Equivalence and Morita Invariant Properties: Applications in the Context of Leavitt Path Algebras; 5.1 Introduction; 5.2 Morita Equivalence for Rings Without a Unit Element: Local Rings at Elements; 5.3 Applications to Morita Invariant Properties; 5.4 Applications in the Context of Leavitt Path Algebras; References; 6 On Commuting U-Operators in Jordan Algebras; 6.1 An Introduction; 6.2 A Counter-Example; 6.3 The Non-degenerate Case; References; Part II Contributed Talks
7 Gradings on Algebras over Algebraically Closed Fields7.1 Introduction; 7.2 Gradings; 7.3 Main Results; References; 8 On the Set of Artinian Subrings of Infinite Products of Rings; 8.1 Introduction; 8.2 Artinian Subrings of an Infinite Product of Rings; 8.3 The Set of Subrings Which Are Directed Unions of Artinian Subrings; References; 9 Noncommutative Gröbner Basis over a Divisible and Annihilable Ring; 9.1 Introduction; 9.2 Preliminaries; 9.2.1 D-A Rings; 9.2.2 Admissible Orderings; 9.3 Non Commutative Gröbner Bases; 9.3.1 Reduction; 9.3.2 A-polynomials