УК гд а Уж × в
УК гд а Уж × в
УК гд а Уж × в
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ÒØÓÒ¿º¿º¿ÌÖØÒ<strong>×</strong>ÙÐÖÓÓÑÔÐÜ<strong>×</strong>ѹ<strong>×</strong>ÑÔÐÄÐÖg<strong>×</strong>Ø ÔØÖ¿ºÃÅÄÐÖ<strong>×</strong><br />
ÓÑÔÐÜ<strong>×</strong>Ù<strong>×</strong>ÔhÓgÛØØÓÐÐÓÛÒÔÖÓÔÖØ<strong>×</strong> 0¸ h¸<br />
ÓÒØÓÒ(i)<strong>×</strong>Ý<strong>×</strong>ØØh<strong>×</strong>ÓÑÑÙØØÚ<strong>×</strong>ÙÐÖÓg¸ÒÓÒØÓÒ(ii)<strong>×</strong>Ý<strong>×</strong>ØØØ<br />
´µÓÖÐÐh 1Òh h¸h<strong>×</strong>ÓÒÐÞк<br />
2Òh¸[h 1 , h 2 ] =<br />
´µÓÖÐÐx ∈ h¸ØÒx ÓÒØÓÒ(iii)<strong>×</strong>Ý<strong>×</strong>h<strong>×</strong>ÓÒÐÞиÒ<strong>×</strong>ÒÐÐØh∈hÓÑÑÙظØh³<strong>×</strong><br />
´µÓÖÐÐh ∈<br />
ØÖÛ<strong>×</strong>ÓÒÐÝÓÒÐÑÒظhº<br />
<strong>×</strong>ÑÜÑÐÐÝÓÑÑÙØØÚºÁØ<strong>×</strong>ØÙ<strong>×</strong>¸ØÒÓÖÑÐÞÖN ÒÖÓÓØ<strong>×</strong>Ô<strong>×</strong>ÒÒ<strong>×</strong>ÓÐÐÓÛ<strong>×</strong> ÖØÒ<strong>×</strong>ÙÐÖºÏØØÓÚÒÖÐÒØÓÒÓØÖØÒ<strong>×</strong>ÙÐÖ¸ØÖÓÓØ<strong>×</strong> ÌÖÒÓÓÑÔÐÜ<strong>×</strong>ѹ<strong>×</strong>ÑÔÐÄÐÖg<strong>×</strong>ÒØÓØÑÒ<strong>×</strong>ÓÒÓØ<strong>×</strong><br />
g<br />
Ð<strong>×</strong>ÓÓÑÑÙظÒØÙ<strong>×</strong>ØÝÖÐ<strong>×</strong>ÓÓÒÐÞÐ<strong>×</strong>ÑÙÐØÒÓÙ<strong>×</strong>ÐݺÓÖØ<strong>×</strong>Ósl(2, C)<br />
ÒØÓÒ¿º¿ºÖÓÓØÓ<strong>×</strong>ѹ<strong>×</strong>ÑÔÐÄÐÖg´ÛØÖ<strong>×</strong>ÔØØÓØÖØÒ<strong>×</strong>Ù¹<br />
gÛØ ∗<strong>×</strong>ÙØØØÖÜ<strong>×</strong>Ø<strong>×</strong>ÒÓÒ¹ÞÖÓÐÑÒØ ÐÖhµ<strong>×</strong>ÒÓÒ¹ÞÖÓÐÒÖÙÒØÓÒÐα∈h<br />
ËÓ¸ÖÓÓØ<strong>×</strong>Ù<strong>×</strong>Ø´ÒÓÒ¹ÞÖÓµÓÐÐØÓÒÓ<strong>×</strong>ÑÙÐØÒÓÙ<strong>×</strong>ÒÚÐÙ<strong>×</strong>ÓÖØh³<strong>×</strong>ºÌ<strong>×</strong>ØÓ<br />
hº<br />
x ∈<br />
ÓÖÐÐh ∈<br />
ÖÐØÓÒ<strong>×</strong>ØÛÒØÐÑÒØ<strong>×</strong>¸ÛÒÒÓÛÜÔÖ<strong>×</strong><strong>×</strong>Ø<strong>×</strong>ÑÒÓÖÑØÓÒ¸Ù<strong>×</strong>ÒØÓÒÔØ<br />
α<strong>×</strong>ÐÐÖÓÓØÚØÓÖ´ÓÖØÖÓÓØαµº<br />
C)ÒÛÓÖÒÓÙØØÚÖÓÙ<strong>×</strong>ÓÑÑÙØØÓÒ ÐÐÖÓÓØ<strong>×</strong><strong>×</strong>ÒÓØLºÌÖÓÓØ<strong>×</strong>Ôg α<strong>×</strong>Ø<strong>×</strong>ÔÓÐÐx∈gÓÖÛ[h, x]<br />
ÓÖÐÐh∈hºÒÐÑÒØÓg 2¸ÒØ<br />
ZØÓÖÖ<strong>×</strong>ÔÓÒÒÖÓÓØÚØÓÖº <strong>×</strong>ÔÝØÚÖÓÙ<strong>×</strong>ÓÑÑÙØØÓÒÖÐØÓÒ<strong>×</strong>¸ÛÛÓÐÓÛºÀÖ¸αÒÓØ<strong>×</strong>ØÖÓÓØÒ<br />
C)ºÚÒØÚÖÓÙ<strong>×</strong>ÖÓÓØ<strong>×</strong><strong>×</strong>ÒÓÙØÓ<br />
ÓÒØÓØ<strong>×</strong><strong>×</strong>ÐÑÒØ<strong>×</strong>Ósl(3, ÓÖÓÓØÚØÓÖ<strong>×</strong>¸<strong>×</strong>ÓÐÐÓÛ<strong>×</strong>ºÌÚØÓÖ<strong>×</strong>x iÒy iÖÒÚØÓÖ<strong>×</strong>ÓÖh 1Òh ÓÐÐØÓÒÓØÒÚÐÙ<strong>×</strong>ÖØÖÓÓØ<strong>×</strong>ÓÖsl(3,<br />
<br />
[h,<br />
g¸[h, x] = 0ÓÖÐÐh ∈<br />
∈<br />
x] = α(h)x ,<br />
(h) = {x ∈ g|[x, h] ⊆ h}ÓhÒgº<br />
= α(h)x
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