УК гд а Уж × в
УК гд а Уж × в
УК гд а Уж × в
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ÔØÖ¿ºÃÅÄÐÖ<strong>×</strong><br />
ØÖØÑÒ<strong>×</strong>ÓÒØÓÒ<strong>×</strong>Ò<strong>×</strong>ÐØÓÒÓÒØ<strong>×</strong>ÔVºÏÐ<strong>×</strong>ÓÒØÖØÓÒÓÒ<br />
<strong>×</strong>3ÑØÖ<strong>×</strong>ØÓØÓÒØ<strong>×</strong><strong>×</strong>ÔºÏÒÐÒÖÓÔÖØÓÖ<strong>×</strong>Ó<br />
ÑÒ<strong>×</strong>ÓÒØÓØÓÒØ<strong>×</strong>ÔVÒÖ<strong>×</strong>ÙØØØÝÖÔÖ<strong>×</strong>ÒØØØÓÒÓSO(3)ÓÒ<br />
VØÓ<strong>×</strong>ÙØØØÖÓÙÔØÓÒÓSO(3)<strong>×</strong>ØÙÐÐÝÔØÙÖÓÒVºÌÙ<strong>×</strong>¸ÛØÛÒ <strong>×</strong>ÑÔÖÓÑSO(3)ØÓØ<strong>×</strong>ÔÓÒÚÖØÐÐÒÖÓÔÖØÓÖ<strong>×</strong>ØØÖÓØÔÔÖÓÔÖØ<br />
ÓÒÒÒÓØÓÚÓÙ<strong>×</strong>ÐÝÙ<strong>×</strong>Ø3 VºÌ<strong>×</strong><strong>×</strong>ØÓÖÔÖ<strong>×</strong>ÒØØÓÒÓÖÓÙÔºÄØÙ<strong>×</strong>ÒÓÛÑØ<strong>×</strong>ÑÓÖÔÖ<strong>×</strong><br />
ÒعÑÒ<strong>×</strong>ÓÒÐÖÔÖ<strong>×</strong>ÒØØÓÒÓgÓÒV<strong>×</strong>ÓÒØÒÙÓÙ<strong>×</strong>ÓÑÓÑÓÖÔ<strong>×</strong>ÑρÓÄ <strong>×</strong>ØÖØÒÛØÓÖÑÐÒØÓÒÓØÖÔÖ<strong>×</strong>ÒØØÓÒÓÄÐÖº ÒØÓÒ¿º¿º½ÄØVÚØÓÖ<strong>×</strong>ÔÓÚÖÐC¸ÒÐØgÄÐÖº<br />
→ÒKVºρ<strong>×</strong>ØÓC¹ÐÒÖÒ<strong>×</strong>ØÓ<strong>×</strong>Ø<strong>×</strong>Ý<br />
ÏÛÐд<strong>×</strong>ÓÑÓ<strong>×</strong>ØÙØÓÖ<strong>×</strong>µÐÐVØÖÔÖ<strong>×</strong>ÒØØÓÒÛÒÛÑÒØÖÔÖ<strong>×</strong>ÒØØÓÒ ´¿ºµ ÐÖ<strong>×</strong>ρ : g<br />
ÑÒ<strong>×</strong>ÓÒÓØÖÔÖ<strong>×</strong>ÒØØÓÒ<strong>×</strong>ÒØÓØÑÒ<strong>×</strong>ÓÒÓØÚØÓÖ<strong>×</strong>ÔVº WÓÖÐÐw∈WÒ<br />
∈ g .<br />
Ì<strong>×</strong>ØÛÝØÓÙÒÖ<strong>×</strong>ØÒØØÓÖÝÓÖÔÖ<strong>×</strong>ÒØØÓÒ<strong>×</strong>ÓÖÓÙÔÓÖÐÖ<strong>×</strong>Ý<br />
gºÖÔÖ<strong>×</strong>ÒØØÓÒÛØÒÓÒÓÒ¹ØÖÚÐÒÚÖÒØ<strong>×</strong>Ù<strong>×</strong>Ô<strong>×</strong><strong>×</strong>ÐÐÖÖÙкÌ<br />
ρ : g<br />
C)ÒØÐ<strong>×</strong>ÓÖØÐݸÙØÓÖØØÛÒØÛÜÑÔÐ<strong>×</strong>ÛÜ<strong>×</strong>ØÓÖÒÝÄ C)Ò<br />
→ÒKVº<strong>×</strong>Ù<strong>×</strong>ÔWÓV<strong>×</strong>ÐÐÒÚÖÒØρ(g)w ÐÐg∈<br />
ÓÒØÑÔÔÒºÊÐÐØØØÛ<strong>×</strong>Ò<strong>×</strong>ØÑÔ ÐÖº ÏÚÐÖÝ<strong>×</strong>ÒÑÔÐØÐÝÒÜÑÔÐÓÖÔÖ<strong>×</strong>ÒØØÓÒÒÕº´¿º¿µØØÓØ<br />
ÐÓÓÒØ<strong>×</strong>ÓÑÜÑÔÐ<strong>×</strong>ºÏÛÐÐ<strong>×</strong>ØÙÝØÖÔÖ<strong>×</strong>ÒØØÓÒ<strong>×</strong>ÓØÄÐÖ<strong>×</strong>sl(2,<br />
sl(3,<br />
ÚÒÝØÓÖÑÙÐ ´¿ºµ<br />
´¿ºµ<br />
:g→ÒCg .<br />
ØÓÒØÖÔÖ<strong>×</strong>ÒØØÓÒºÁØ<strong>×</strong>ØÖÔÖ<strong>×</strong>ÒØØÓÒÓØÄÐÖgØÒÓÒØ<strong>×</strong>к ÓÑÔÖÒ´¿ºµÛØ´¿º¿µ¸Û<strong>×</strong>Øس<strong>×</strong>ÖÔÖ<strong>×</strong>ÒØØÓÒÛÖØ<strong>×</strong>ÔV<strong>×</strong>ØÒ ØÓgº³<strong>×</strong>ÄÐÖÓÑÓÑÓÖÔ<strong>×</strong>ÑÒ<strong>×</strong>¸ØÖÓÖÖÔÖ<strong>×</strong>ÒØØÓÒÓg¸ÐÐ<br />
x(y)<br />
ÒÓØÖÖÔÖ<strong>×</strong>ÒØØÓÒØØÜ<strong>×</strong>Ø<strong>×</strong>ÓÖÐÐÄÐÖ<strong>×</strong><strong>×</strong>ØØÖÚÐÖÔÖ<strong>×</strong>ÒØØÓÒºÁg <strong>×</strong>ÄÐÖÓn <strong>×</strong> nÑØÖ<strong>×</strong>ÓÚÖCØÒØØÖÚÐÖÔÖ<strong>×</strong>ÒØØÓÒρ <br />
ρ([x, y]) = ρ(x)ρ(y) − ρ(y)ρ(x) ÓÖÐÐx, y<br />
∈<br />
= [x, y] .<br />
C)<strong>×</strong> : g → gl(1,
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