| Description |
1 online resource (369 p.) |
| Contents |
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 |
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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 |
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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 |
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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 |
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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 |
| Notes |
Description based upon print version of record |
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5.4. Quadratic H -algebras |
| Subject |
Algebra.
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algebra.
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| Form |
Electronic book
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| ISBN |
9781119818168 |
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1119818168 |
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