Noncommutative invariants of bialgebras

Suppose that H is a bialgebra over a field C and R = CV is the tensor algebra of the C-space V endowed with the structure of an H-module algebra, so that V is a submodule of the H-module R, R^H is the algebra of H-invariants, and W, the support of the algebra R^H, is the smallest subspace of the C-space V such that . The main result of the paper is the theorem stating that if the algebra of H-invariants R^H is finitely generated, then the support of R^H is a finite-dimensional submodule of the H-module V, whose elements are H-semi-invariants of the same weight.Translated fromAlgebra i Logika, Vol. 33, No. 6, pp. 654–680, November–December, 1994.Supported by the Soros Foundation (grant RPS000) and the Russian Foundation for Fundamental Research (grant No. 93-01-16171).