Journal of Prime Research in Mathematics

# $$G_p$$-Finiteness of tensor product

M.S. Balasubramani
Deptartment of Mathematics, University of Calicut, Kerala – 673 635.
K. T. Ravindran
PG Department and Research Centre in Mathematics, Payyanur College, Payyanur, Kerala – 670 307.

$$^{1}$$Corresponding Author: msbalaa@rediffmail.com

### Abstract

In this paper we introduce $$G_P$$ finiteness of a Von-Neumann algebra and we define a G-dimension function. Then we prove a result on tensor product of fixed point algebra under group of automorphisms and finally verify a result under which the tensor product is $$G_P$$ finite.

#### Keywords:

Von Neumann algebra M, the fixed point algebra under groups of automorphisms $$M^{G}$$, G- central support, ultra weak continuous.