• Samuel M. Vovsi
Part of the Progress in Mathematics book series (PM, volume 17)


This section is devoted to a very concrete problem. As usual, let K be a commutative ring with 1, and let UTn (K) = UTn and Tn (K) = Tn be the full unitriangular and triangular matrix groups of degree n over K, respectively. Denote by
$$ {\rm{u}}{{\rm{t}}_{\rm{n}}}{\rm{ = u}}{{\rm{t}}_{\rm{n}}}\left( {\rm{K}} \right){\rm{ = }}\left( {{{\rm{K}}^{\rm{n}}}{\rm{,U}}{{\rm{T}}_{\rm{n}}}\left( {\rm{K}} \right)} \right){\rm{ and }}{{\rm{t}}_{\rm{n}}}{\rm{ = }}{{\rm{t}}_{\rm{n}}}\left( {\rm{K}} \right){\rm{ = }}\left( {{{\rm{K}}^{\rm{n}}}{\rm{,}}{{\rm{T}}_{\rm{n}}}\left( {\rm{K}} \right)} \right) $$
their canonical representations in the free K-module of rank n. These classical objects deserve to be studied from various positions; in particular, from the standpoint of identities and varieties. Naturally, the first problem one should solve here is the following: to describe the varieties var utn and var tn or, equivalently, to find bases for the identities of the representations utn and tn.


Radical Class Nilpotent Group Wreath Product Faithful Representation Dedekind Domain 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Birkhäuser Boston 1981

Authors and Affiliations

  • Samuel M. Vovsi
    • 1
  1. 1.Riga Polytechnic InstituteRigaUSSR

Personalised recommendations