National Academy of Sciences of Belarus

ZALESSKY Alexander Efimovich

Alexander Efimovich Zalessky (b. 17.01.1939, Minsk), mathematician. Corresponding Member of the National Academy of Sciences of Belarus (1991). Doctor of Physico-Mathematical Sciences (1978), Professor (1986).

Scientific works on the theory of linear groups, group rings of infinite groups and the theory of group representations. Investigated the subgroups of linear groups above the bodies. Gave a classification of finite irreducible groups generated by reflections, as well as arbitrary groups of degrees 4 and 5 over finite fields. Received a refutation of the hypothesis about the freedom of the algebra of invariants of derived groups generated by reflections. He laid the foundations of the theory of ideals in group rings of infinite soluble groups. Solved the problem of Kaplanovsky about the ideponents of group rings, and also the problem of Feys about the existence of simple Noetherian rings with zero divisors, but without ideponents. He developed methods for studying the eigenvalues ​​of matrices in representations of finite Lie-type groups. He proved the existence of an eigenvalue 1 for the image of each semisimple element in any complex representation of groups of Lie types G (2), F (4), E (6) and their twisted analogues. Investigated the behavior of the reduction modulo p basic Weyl representations of finite classical groups. On this basis, a new method is proposed for finding formulas for the decomposition numbers of certain types of representations of the indicated groups during the reduction modulo an intrinsic characteristic. Developed the theory of ideals of group algebras of locally finite groups.

Author of more than 100 scientific papers.

Major papers:

  1. Алгебра и алгебраическая геометрия в работах математиков Белоруссии. Мн., 1979 (совм. с В.С. Конюхом).
  2. Конечные линейные группы, порожденные отражателями, над полями нечетных характеристик. Мн., 1979 (совм. с В.Н. Сережкиным).
  3. Модулярные подставочные представления и фрагмент матрицы разложения для симплектической и специальной линейной группы над конечным полем. Мн., 1987 (совм. с И.Д. Супруненко).
  4. Some papers of Alexander Zalesskii.