It was shown by A.V.Mikhalev and I.A.Pinchuk in [MP] that the second homology group H2(st(m,n,R)) of the Steinberg Lie superalgebra st(m,n,R) is trivial for m+n ≥ 5. In this paper, we will work out H2(st(m,n,R)) explicitly for m + n = 3, 4. Introduction Steinberg Lie algebras stn(R) play an important role in (additive) algebraic K-theory. They have been studied by many people (see [L] and [GS],...

We determine the finite simple groups of Lie type of characteristic p, for which the Steinberg character lies in the principal `-block for every prime ` 6= p dividing the order of the group. In [1, Corollary 4.4], Bessenrodt, Malle, and Olsson determine the finite simple groups of Lie type having a non-trivial irreducible character which is in the principal `-block for all primes ` dividing the...

The first four reviews in this series (Steinberg, D. 2004. J. Lipid Res. 45: 1583-1593; Steinberg, D. 2005. J. Lipid Res. 46: 179-190; Steinberg, D. 2005. J. Lipid Res. 46: 2037-2051; Steinberg, D. 2006. J. Lipid Res. 47: 1-14) traced the gradual accumulation of evidence, evidence of several different kinds, supporting the lipid hypothesis. They tracked the history from Anitschkow's 1913 classi...