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Restricted one-dimensional central extensions of restricted simple Lie algebras
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We study the restricted one-dimensional central extensions of an arbitrary finite dimensional restricted simple Lie algebra for mmlsi1" class="mathmlsrc">mulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379516304542&_mathId=si1.gif&_user=111111111&_pii=S0024379516304542&_rdoc=1&_issn=00243795&md5=9925cf9a56de4fdf980689b6b6e5d8a0" title="Click to view the MathML source">p≥5mathContainer hidden">mathCode"><math altimg="si1.gif" overflow="scroll"><mi>pmi><mo>≥mo><mn>5mn>math>. For mmlsi15" class="mathmlsrc">mulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379516304542&_mathId=si15.gif&_user=111111111&_pii=S0024379516304542&_rdoc=1&_issn=00243795&md5=5112e2c0bc785bfaad37777b1554dbac" title="Click to view the MathML source">H2(g)=0mathContainer hidden">mathCode"><math altimg="si15.gif" overflow="scroll"><msup><mrow><mi>Hmi>mrow><mrow><mn>2mn>mrow>msup><mo stretchy="false">(mo><mi mathvariant="fraktur">gmi><mo stretchy="false">)mo><mo>=mo><mn>0mn>math>, we explicitly describe the cocycles spanning mmlsi3" class="mathmlsrc">mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379516304542&_mathId=si3.gif&_user=111111111&_pii=S0024379516304542&_rdoc=1&_issn=00243795&md5=99d28f3476116a996a693eadf6dbcbb5">mg class="imgLazyJSB inlineImage" height="18" width="44" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0024379516304542-si3.gif">mathContainer hidden">mathCode"><math altimg="si3.gif" overflow="scroll"><msubsup><mrow><mi>Hmi>mrow><mrow><mo>⁎mo>mrow><mrow><mn>2mn>mrow>msubsup><mo stretchy="false">(mo><mi mathvariant="fraktur">gmi><mo stretchy="false">)mo>math>, and in the case mmlsi13" class="mathmlsrc">mulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379516304542&_mathId=si13.gif&_user=111111111&_pii=S0024379516304542&_rdoc=1&_issn=00243795&md5=9b38467f3e5d71dbb0e39bf9dbe4f5a3" title="Click to view the MathML source">H2(g)≠0mathContainer hidden">mathCode"><math altimg="si13.gif" overflow="scroll"><msup><mrow><mi>Hmi>mrow><mrow><mn>2mn>mrow>msup><mo stretchy="false">(mo><mi mathvariant="fraktur">gmi><mo stretchy="false">)mo><mo>≠mo><mn>0mn>math>, we give a procedure to describe a basis for mmlsi3" class="mathmlsrc">mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379516304542&_mathId=si3.gif&_user=111111111&_pii=S0024379516304542&_rdoc=1&_issn=00243795&md5=99d28f3476116a996a693eadf6dbcbb5">mg class="imgLazyJSB inlineImage" height="18" width="44" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0024379516304542-si3.gif">mathContainer hidden">mathCode"><math altimg="si3.gif" overflow="scroll"><msubsup><mrow><mi>Hmi>mrow><mrow><mo>⁎mo>mrow><mrow><mn>2mn>mrow>msubsup><mo stretchy="false">(mo><mi mathvariant="fraktur">gmi><mo stretchy="false">)mo>math>.

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