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(/usr/share/texmf-texlive/tex/latex/base/ulasy.fd File: ulasy.fd 1998/08/17 v2.2e LaTeX symbol font definitions ) LaTeX Font Info: Try loading font information for U+msa on input line 101. (/usr/share/texmf-texlive/tex/latex/amsfonts/umsa.fd File: umsa.fd 2002/01/19 v2.2g AMS font definitions ) LaTeX Font Info: Try loading font information for U+msb on input line 101. (/usr/share/texmf-texlive/tex/latex/amsfonts/umsb.fd File: umsb.fd 2002/01/19 v2.2g AMS font definitions ) Overfull \hbox (4.89955pt too wide) in paragraph at lines 109--117 \OT1/cmr/m/n/10.95 mod-ule over Gra^^Y-mann al-ge-bra of dif-fer-en-tial forms al-lows a novel/algo- [] Overfull \hbox (29.59772pt too wide) in paragraph at lines 122--126 \OT1/cmr/bx/n/12 Keywords: \OT1/cmr/m/n/12 uni-ver-sal Gra^^Y-mann mod-ule, Nij enhuis-Richardson al-ge-bra, Fr^^?olicher- [] (./SandBoxNijenhuis.toc [1 ]) \tf@toc=\write4 \openout4 = `SandBoxNijenhuis.toc'. [2] Underfull \vbox (badness 10000) has occurred while \output is active [] [3] [4] [5] Overfull \hbox (10.10956pt too wide) in paragraph at lines 331--334 \OT1/cmr/bx/n/12 3.2 Def-i-ni-tion \OT1/cmr/m/n/12 (Ger-sten-haber al-ge-bra)\O T1/cmr/bx/n/12 . \OT1/cmr/m/n/12 The $\U/msb/m/n/12 Z$\OT1/cmr/m/n/12 -graded L eib-niz al-ge-bra $(\OMS/cmsy/m/n/12 \\OML/cmm/m/it/12 ; \OT1/cmr/m/n/12 [\OMS/ cmsy/m/n/12 ^^A\OML/cmm/m/it/12 ; \OMS/cmsy/m/n/12 ^^A\OT1/cmr/m/n/12 ])$ [] Overfull \hbox (9.33295pt too wide) in paragraph at lines 348--353 \OT1/cmr/m/n/12 graded en-do-mor-phisms $\OML/cmm/m/it/12 A; B; C \OMS/cmsy/m/n /12 2 []\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 M[]\OT1/cmr/m/n/12 )\OML/cmm/m/it/12 :$ \OT1/cmr/m/n/12 We ab-bre-vi-ate $(\OMS/cmsy/m/n/12 ^^@\OT1/cmr/m/n/12 1)[]$ [] [6] Overfull \hbox (18.62721pt too wide) in paragraph at lines 391--395 \OT1/cmr/m/n/12 The deriva-tion $\OML/cmm/m/it/12 d \OMS/cmsy/m/n/12 2 [][]\OT1 /cmr/m/n/12 (\OMS/cmsy/m/n/12 F\OML/cmm/m/it/12 ; M\OT1/cmr/m/n/12 )$ has the u ni-ver-sal prop-erty: for $\OML/cmm/m/it/12 D \OMS/cmsy/m/n/12 2 [][]\OT1/cmr/m /n/12 (\OMS/cmsy/m/n/12 F\OML/cmm/m/it/12 ; M[]\OT1/cmr/m/n/12 )\OML/cmm/m/it/1 2 ;$ [] [7] [8] [9] [10] [11] [12] Overfull \hbox (0.38345pt too wide) in paragraph at lines 605--612 []\OT1/cmr/m/n/12 Another im-por-tant easy con-se-quence of Def-i-ni-tion []-[] is the graded [] [13] [14] Overfull \hbox (1.44751pt too wide) in paragraph at lines 705--708 []\OT1/cmr/m/n/12 A Frobe-nius $\OMS/cmsy/m/n/12 F$\OT1/cmr/m/n/12 -algebra is both Frobe-nius al-ge-bra and Frobe-nius co-algebra [] [15] Overfull \hbox (23.81177pt too wide) in paragraph at lines 746--746 []\OT1/cmr/bx/n/17.28 Frobenius sub-al-ge-bra of Nijenhuis-Richardson [] [16] LaTeX Font Info: Try loading font information for OMS+cmr on input line 785. (/usr/share/texmf-texlive/tex/latex/base/omscmr.fd File: omscmr.fd 1999/05/25 v2.5h Standard LaTeX font definitions ) LaTeX Font Info: Font shape `OMS/cmr/m/n' in size <12> not available (Font) Font shape `OMS/cmsy/m/n' tried instead on input line 785. [17] [18] [19] Underfull \hbox (badness 10000) in paragraph at lines 927--930 \OT1/cmr/m/n/12 http://math.ucr.edu/home/baez/week174.html, [] [20] Underfull \hbox (badness 2582) in paragraph at lines 970--973 []\OT1/cmr/m/n/12 Frobenius Fer-di-nand Georg (1903). The-o-rie der hy-per-kom- plexen [] [21] [22] Underfull \hbox (badness 3209) in paragraph at lines 1005--1008 []\OT1/cmr/m/n/12 Kocik Jerzy, (1997). Rel-a-tivis-tic ob-server and Maxwell's equa- [] Underfull \hbox (badness 4429) in paragraph at lines 1005--1008 \OT1/cmr/m/n/12 tions: an ex-am-ple of a non-principal Ehres-mann con-nec-tion, [] [23] Underfull \hbox (badness 2644) in paragraph at lines 1054--1057 []\OT1/cmr/m/n/12 Oziewicz Zbig-niew, (1997). Clif-ford al-ge-bra and uni-ver-s al Hopf [] Underfull \hbox (badness 5446) in paragraph at lines 1054--1057 \OT1/cmr/m/n/12 al-ge-bra, Czechoslo-vak Jour-nal of Physics \OT1/cmr/bx/n/12 4 7 \OT1/cmr/m/n/12 (12) 1267--1274, [] [24] [25] (./SandBoxNijenhuis.aux) LaTeX Warning: There were multiply-defined labels. ) Here is how much of TeX's memory you used: 3657 strings out of 94075 42315 string characters out of 1165177 131931 words of memory out of 1500000 6895 multiletter control sequences out of 10000+50000 19657 words of font info for 83 fonts, out of 1200000 for 2000 648 hyphenation exceptions out of 8191 30i,24n,24p,250b,295s stack positions out of 5000i,500n,6000p,200000b,5000s Output written on SandBoxNijenhuis.dvi (25 pages, 90964 bytes).