. We compute the cohomology algebra of P (1), the subalgebra of the Steenrod algebra generated by P 1 and P p . This completes a partial result given by Arunas Liulevicius in 1962 and provides explicit representatives in the cobar construction for all but one of the algebra generators. Introduction. In 1962, Arunas Liulevicius used a twisted tensor product of two minimal resolutions to compute the cohomology of a certain Hopf algebra with two algebra generators. Up to a regrading, this Hopf algebra is the sub-Hopf algebra of the mod-p Steenrod algebra generated by P 1 and P p and is usually denoted P (1). Its cohomology is of interest in relation to the cohomology of the Steenrod algebra, which is the E 2 term of the Adams spectral sequence. Liulevicius' results are not complete, however, since he only gives algebra generators and relations in the case p = 2. For p = 3, he gives algebra generators and an incomplete list of relations, and for p ? 3 he only gives module gene...
After finalizing the plan of operation in 1980, which was based upon the decision to
unifying various Lithuanian scholarly and education organizations under the umbrella
of one institution, the Lithuanian Research and Studies Center was founded in
1981. Among the founders were: Dr. Adolfas Damusis, the historian Jonas
Dainauskas, Director of the Lithuanian World Archives Ceslovas Grincevicius, Rev.
Vaclovas Gutauskas, S.J., Bronius Kviklys, Dr. Arunas Liulevicius, Dr. Jonas
Rackauskas, and Dr. Robertas Vitas.
Liulevicius earned his Ph.D. in 1960 from the University of Chicago under advisor . Halmos was at Chicago from 1946 to 1961 and he and Liulevicius would have first met there. Liulevicius is an algebraic topologist who has written and edited several books in his field, including Algebraic Topology (AMS Proceedings of Symposia in Pure Mathematics, 1971) and Cobordism and Homology (University of São Paulo, 1969). He seems to have spent most of his career at the University of Chicago, advising Ph.D. students there at least from 1965 to 1975, and he is now Professor Emeritus at Chicago. Additional information about Arunas Liulevicius would be appreciated. (Sources: Mathematics Genealogy Project, , )