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    Scientists / Open questions

    埃菲姆·泽尔曼诺夫

    Efim Zelmanov

    群论、李代数、非结合代数

    1994 年菲尔兹奖

    8 个问题

    1. Finite exponent of compact torsion groups (bounded exponent of periodic compact groups)

    2. Stable nil algebras of finite Gelfand–Kirillov dimension and the completion of stability-preserving embedding theorems

    3. Is the endomorphism ring of a finitely generated module over an affine Noetherian PI-ring a Jacobson ring, and must the center of such a ring be Jacobson?

    4. Classifying filtered deformations and the completion identification A∗=G∗A^*=G^* for the type I and integer-parameter type IV Novikov prototypes of Osborn-Zelmanov

    5. Extensions, automorphisms, and involutions of Leavitt path algebras of polynomial growth: completing the ideal-chain structure theory

    6. Speciality of Kantor doubles of Jordan brackets: sufficiency of Shestakov's identity (4)

    7. Indecomposable finite-dimensional unital bimodules over the Jordan superalgebra D(0)D(0), the unitization of the Kaplansky superalgebra K3K_3

    8. Zelmanov's Conjecture 4.11: is the linearized algebra J⊗FEJ\otimes_F E of a quadratic Jordan PI-algebra nil of bounded index in characteristic p>0p>0?

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