Algebra and Applications 1 Non-Associative Algebras and Categories.

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Makhlouf, Abdenacer
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Newark : John Wiley & Sons, Incorporated, 2021.
Temas:
Algebra.
Algèbre.
algebra.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Cover
  • Half-Title Page
  • Title Page
  • Copyright Page
  • Contents
  • Foreword
  • 1 Jordan Superalgebras
  • 1.1. Introduction
  • 1.2. Tits-Kantor-Koecher construction
  • 1.3. Basic examples (classical superalgebras)
  • 1.4. Brackets
  • 1.5. Cheng-Kac superalgebras
  • 1.6. Finite dimensional simple Jordan superalgebras
  • 1.6.1. Case F is algebraically closed and char F = 0
  • 1.6.2. Case char F = p > 2, the even part J0̄ is semisimple
  • 1.6.3. Case char F = p > 2, the even part J0̄ is not semisimple
  • 1.6.4. Non-unital simple Jordan superalgebras
  • 1.7. Finite dimensional representations
  • 1.7.1. Superalgebras of rank ≥ 3
  • 1.7.2. Superalgebras of rank ≤ 2
  • 1.8. Jordan superconformal algebras
  • 1.9. References
  • 2 Composition Algebras
  • 2.1. Introduction
  • 2.2. Quaternions and octonions
  • 2.2.1. Quaternions
  • 2.2.2. Rotations in three(and four-) dimensional space
  • 2.2.3. Octonions
  • 2.3. Unital composition algebras
  • 2.3.1. The Cayley-Dickson doubling process and the generalized Hurwitz theorem
  • 2.3.2. Isotropic Hurwitz algebras
  • 2.4. Symmetric composition algebras
  • 2.5. Triality
  • 2.6. Concluding remarks
  • 2.7. Acknowledgments
  • 2.8. References
  • 3 Graded-Division Algebras
  • 3.1. Introduction
  • 3.2. Background on gradings
  • 3.2.1. Gradings induced by a group homomorphism
  • 3.2.2. Weak isomorphism and equivalence
  • 3.2.3. Basic properties of division gradings
  • 3.2.4. Graded presentations of associative algebras
  • 3.2.5. Tensor products of division gradings
  • 3.2.6. Loop construction
  • 3.2.7. Another construction of graded-simple algebras
  • 3.3. Graded-division algebras over algebraically closed fields
  • 3.4. Real graded-division associative algebras
  • 3.4.1. Simple graded-division algebras
  • 3.4.2. Pauli gradings
  • 3.4.3. Commutative case
  • 3.4.4. Non-commutative graded-division algebras with one-dimensional homogeneous components
  • 3.4.5. Equivalence classes of graded-division algebras with one-dimensional homogeneous components
  • 3.4.6. Graded-division algebras with non-central two-dimensional identity components
  • 3.4.7. Graded-division algebras with four-dimensional identity components
  • 3.4.8. Classification of real graded-division algebras, up to isomorphism
  • 3.5. Real loop algebras with a non-split centroid
  • 3.6. Alternative algebras
  • 3.6.1. Cayley-Dickson doubling process
  • 3.6.2. Gradings on octonion algebras
  • 3.6.3. Graded-simple real alternative algebras
  • 3.6.4. Graded-division real alternative algebras
  • 3.7. Gradings of fields
  • 3.8. References
  • 4 Non-associative C*-algebras
  • 4.1. Introduction
  • 4.2. JB-algebras
  • 4.3. The non-associative Vidav-Palmer and Gelfand-Naimark theorems
  • 4.4. JB*-triples
  • 4.5. Past, present and future of non-associative C*-algebras
  • 4.6. Acknowledgments
  • 4.7. References
  • 5 Structure of H -algebras
  • 5.1. Introduction
  • 5.2. Preliminaries: aspects of the general theory
  • 5.3. Ultraproducts of H -algebras

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