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Journals and Conferences
We study Kuzmin’s conjecture on the index of nilpotency for the variety N il5 of associative nil-algebras of degree 5. Due to Vaughan-Lee  the problem is reduced to that for k-generator N il5-superalgebras, where k ≤ 5. We confirm Kuzmin’s conjecture for 2-generator superalgebras proving that they are nilpotent of degree 15.
We prove the unique solvability of a mixed boundary value problem for the p -Laplace operator by means of variational methods. Using the obtained results, we construct an iterative procedure for solving the Cauchy problem for the p -Laplace operator.
Recently J.A.Anquela, T.Cortés, and H.Petersson  proved that for elements x, y in a non-degenerate Jordan algebra J , the relation x ◦ y = 0 implies that the U -operators of x and y commute: UxUy = UyUx. We show that the result may be not true without the assumption on nondegeneracity of J . We give also a more simple proof of the mentioned result in the… (More)
We extend the Jacobson’s Coordinatization theorem to Jordan superalgebras. Using it we classify Jordan bimodules over superalgebras of types Q(n) and JP (n), n ≥ 3. Then we use the Tits-Kantor-Koecher construction and representation theory of Lie superalgebras to treat the remaining case Q(2).
We obtain classification of the irreducible bimodules over the Jordan superalgebraKan(n), the Kantor double of the Grassmann Poisson superalgebra Gn on n odd generators, for all n ≥ 2 and an algebraically closed field of characteristic 6= 2. This generalizes the corresponding result of C.Mart́ınez and E.Zelmanov announced in [MZ2] for n > 4 and a field of… (More)