Graded Simple Jordan Superalgebras of Growth One.

Intro -- Contents -- Introduction -- Statement of the Problem -- Definitions and Notation -- The Main Result -- Structure of the Proof -- Chapter 1. Structure of the Even Part -- 1.1. General results -- Chapter 2. Cartan type -- 2.1. Results -- 2.2. A/I one-sided graded -- Chapter 3. Even Part is Direct Sum of two Loop Algebras -- 3.1. General Results -- 3.2. A = F[t[sup(-n)],t[sup(n)]] -- 3.3. A = F[t[sup(-n1)][sub(1)],t[sup(n1)]sub(1)]] ⊕ F[t[sup(-n2)][sub(2)],t[sup(n2)]sub(2)]] -- 3.4. A = L(G') ⊕ L(G) -- Chapter 4. A is a Loop Algebra -- 4.1. General Results -- Chapter 5. J is a finite dimensional Jordan Superalgebra or a Jordan Superalgebra of a Superform -- 5.1. A is finite dimensional -- 5.2. A/I finite dimensional, I ≠ (0) -- 5.3. A is a Jordan algebra of a bilinear form -- Chapter 6. The Main Case -- 6.1. Splitting Theorem -- 6.2. Structure of J -- Chapter 7. Impossible Cases -- 7.1. I = (0), A = A[sup((1))] ⊕ A[sup((2))] -- A[sup((1))] is a loop algebra, A[sup((2))] is one-sided graded -- 7.2. A = A[sup((1))] ⊕ A[sup((2))], A[sup((1))] is a negatively graded algebra, A[sup((2))] is a positively graded algebra -- 7.3. A = A[sup((1))] ⊕ A[sup((2))] with A[sup((1))] infinite dimensional Jordan algebra of a bilinear form -- 7.4. I ≠ (0), A/I is an infinite dimensional Jordan algebra of a nondegenerate symmetric bilinear form -- 7.5. A = A[sup((1))] ⊕ A[sup((2))], A[sup((1))] is finite dimensional -- A[sup((2))] is a loop algebra -- Bibliography.

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