Celebratio Mathematica

Irving Kaplansky

Kap encounters in Chicago and Berkeley

by Calvin C. Moore

I first “met” Kap math­em­at­ic­ally when I was a gradu­ate stu­dent at Har­vard work­ing in func­tion­al ana­lys­is and read and stud­ied his strik­ing 1951 pa­pers on \( \mathrm{C}^* \)-al­geb­ras in which he defined and ex­plored the prop­er­ties of what he called CCR and GCR al­geb­ras. His al­geb­ra­ic in­sight in­to these ob­jects arising in ana­lys­is turned out to be of sem­in­al im­port­ance and in­deed were years ahead of their time. I also read about what was by then called the Ka­plansky dens­ity the­or­em for von Neu­mann al­geb­ras dat­ing from 1952 and stud­ied his won­der­ful 1948 pa­per on groups with rep­res­ent­a­tions of bounded de­gree and its con­nec­tion with poly­no­mi­al iden­tit­ies.

I was eager to meet this al­geb­ra­ist whose work had been so in­flu­en­tial in my own stud­ies in a very dif­fer­ent field, and I had that op­por­tun­ity when I had a postdoc­tor­al ap­point­ment at Chica­go in 1960–61. However, I soon left Chica­go for Berke­ley, and it was many years be­fore our paths crossed again. When we were plan­ning a full year pro­gram at the Math­em­at­ic­al Sci­ences Re­search In­sti­tute (MSRI) in 1983–84 on the top­ic of in­fin­ite di­men­sion­al Lie al­geb­ras, Kap’s broad and deep in­sight and un­der­stand­ing in al­gebra led us to se­lect him as the chair of the pro­gram com­mit­tee. We also re­cog­nized that his subtle and ef­fect­ive dip­lo­mat­ic skills would be es­sen­tial in­gredi­ents in mak­ing this pro­gram the great suc­cess that it was.

Al­most at the same time, the Board of Trust­ees of MSRI se­lec­ted Kap to suc­ceed Shi­ing-Shen Chern as dir­ect­or of MSRI in 1984. We served to­geth­er at MSRI, he as dir­ect­or and I con­tinu­ing as deputy dir­ect­or for a year be­fore I left MSRI for an ad­min­is­trat­ive post in the Uni­versity of Cali­for­nia. It was a won­der­ful learn­ing and teach­ing ex­per­i­ence for both of us. I learned much from Kap’s wis­dom and ex­per­i­ence, and I in turn tried to con­vey to him what I knew about MSRI op­er­a­tions. I sub­sequently watched more from a dis­tance, and it was clear that MSRI grew and prospered un­der his eight years of ex­cel­lent lead­er­ship as dir­ect­or. He also main­tained a lively re­search pro­gram while serving as dir­ect­or and for many years after step­ping down. We all miss this gen­er­ous and wise man of many tal­ents.