REPRESENTATIONS OF CLASSIFICAL GROUPS AND VARIETIES OF LIE ALGEBRAS

The aim is to investigate the structure of the free Lie algebra and free algebras of the varieties as modules over total linear and symmetric groups. The values of the unspecified characters in the symmetric group on the classes of the adjoined elements corresponding to the product of the equal length independent cycles have been found. The values of the multiplicities for unspecified modules in the homogeneous component of the free Lie algebra have been calculated. The theorem about coincidence of the verbal ideals generated by some variety, free finite-generated Lie algebra over fields of the non-zero characteristic and ideal generated by an action of the universal enveloping Lie algebra for differentiations of the initial free Lie algebra on the same variety has been proved. The representation of the minimal rate homogeneous component for module of the consequences for the polynilpotent identity in the terms of the induced modules has been foundAvailable from VNTIC / VNTIC - Scientific & Technical Information Centre of RussiaSIGLERURussian Federatio