Deep matrices and their Frankenstein actions Kevin McCrimmon

Abstract The algebra of deep matrices E(X,A) is spanned over a coordinate algebra A by “deep matrix units” Ekh parameterized, not by single natural numbers like the standard matrix units Eji , but by all “deep indices” or “heads” h,k (finite strings of natural numbers or some other infinite set X). This algebra has a natural Frankenstein action on the free right A-module V (X,A) with basis of all “bodies” b (infinite sequences or strings), where Ekh chops off head k from the body b and sews on a new head h (replaces an initial string k of b by h): Ekh(kd) = hd, E

k h(b) = 0 if b does not begin with string k.