Third homology of general linear groups

The third homology group of GL_n(R) is studied, where R is a `ring with many units' with center Z(R). The main theorem states that if K_1(Z(R))_Q \simeq K_1(R)_Q, (e.g. R a commutative ring or a central simple algebra), then H_3(GL_2(R), Q) --> H_3(GL_3(R), Q) is injective. If R is commutative, Q can be replaced by a field k such that 1/2 is in k. For an infinite field R (resp. an infinite field R such that R*=R*^2), we get a better result that H_3(GL_2(R), Z[1/2] --> H_3(GL_3(R), Z[1/2]) (resp. H_3(GL_2(R), Z) --> H_3(GL_3(R), Z)) is injective. As an application we study the third homology group of SL_2(R) and the indecomposable part of K_3(R).Comment: 24 pages, Latex, new title, some results are generalized, added reference

Proton modified Pt zeolite fuel cell electrocatalysts

NaY Zeolite is selected as a suitable material to host 1.5 wt% Platinum (Pt) loading on zeolite using ion exchange method (a) Pt(NH3)4(NO3)2 without excess NH4NO3 nitrate and (b) Pt(NH3)4(NO3)2 with excess NH4NO3 nitrate. The structure/reactivity relationship of Pt nanoparticle has been experimentally studied via Nafion@ bound electrodes to investigate the interaction nature of Pt with zeolite and electron transfer using the extended X-ray adsorption fine structure (EXAFS) and Pt particle was predicted at 0.7 – 1.5 (nm). Pt oxides can be electrochemically reduced via a hydrogen ‘spillover’ phenomenon. A highly dispersed small Pt particle distribution can be achieved with excessive H+ ions on zeolite acidic sites

Third homology of general linear groups over rings with many units

For a commutative ring R with many units, we describe the kernel of H_3(inc): H_3(GL_2(R), Z) --> H_3(GL_3(R), Z). Moreover we show that the elements of this kernel are of order at most two. As an application we study the indecomposable part of K_3(R).Comment: 12 pages, Late