Completions of cellular algebras.

Green, R. M and Fan, C. K. (1999) Completions of cellular algebras. Communications in Algebra, 27 (11). pp. 5349-5366. ISSN 0092-7872

Abstract

We introduce procellular algebras, so called because they are inverse limits of finite dimensional cellular algebras as defined by Graham and Lehrer. A procellular algebra is defined as a certain completion of an infinite dimensional cellular algebra whose cell datum is of “proflnite type”. We show how these notions overcome some known obstructions to the theory of cellular agebras in infinite dimensions.