УК гд а Уж × в
УК гд а Уж × в
УК гд а Уж × в
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ØÖÝØÑÓ<strong>×</strong>ØÒÖÐÒ<strong>×</strong>ØÞÓÖØÖØÓØÒÖØÓÖ<strong>×</strong><strong>×</strong> ÔØÖ¿ºÃÅÄÐÖ<strong>×</strong><br />
´¿ºµ<br />
m0ÒÔÙØ<br />
[t α m, t β n] = f αβ γ t γ ⊗ z m+n + (f αβ i ) mnk i .<br />
ÙÒÕÙ<strong>×</strong>ÙØÒ<strong>×</strong>ÓÖÓÖg¸ÒØØ<strong>×</strong>ØÃÐÐÒÓÖÑÓgºÌÙ<strong>×</strong>¸ØÒØÖÐÜØÒ<strong>×</strong>ÓÒ<strong>×</strong> ´ØØ<strong>×</strong>¸ÒØÓÒصÒÒØ<strong>×</strong>ØÖÙØÙÖÓÒ<strong>×</strong>ØÒØ<strong>×</strong><strong>×</strong>ÓÙÐÖÓÑÒÒÚÖÒØØÒ<strong>×</strong>ÓÖ<br />
ÏÑÔÓ<strong>×</strong>ØÓÒ<strong>×</strong>ØÖÒØ<strong>×</strong>ÓÑÒÖÓÑØÂÓÒØØÝÒØØØØØÐÖg<br />
ÓÒÐÝÓÒ¹ÑÒ<strong>×</strong>ÓÒиÒ<strong>×</strong>ÔÖÓÔÓÖØÓÒÐØÓØÃÐÐÒÓÖÑBÓgºÓÖÓÒÚÒÒ¸Û<br />
<strong>×</strong><strong>×</strong>ÙÐÖÓg loop¸ÒÒØ<strong>×</strong>ØÖÙØÙÖÓÒ<strong>×</strong>ØÒØ<strong>×</strong>(f<br />
βºÁØØÙÖÒ<strong>×</strong>ÓÙØØÖ<strong>×</strong><br />
αβ<br />
i ) 00Ò(f i )<br />
ØÓÞÖÓºÆÓÛ¸ÓÖÜÚÐÙÓn¸ØÒÖØÓÖ<strong>×</strong>tα nØÖÒ<strong>×</strong>ÓÖÑÙ<strong>×</strong>ØÐØÒÖØÓÖ<strong>×</strong>t αβºÌ<strong>×</strong>Ú<strong>×</strong>Ø ÓØÓÒØÖÔÖ<strong>×</strong>ÒØØÓÒÓgÛØÖ<strong>×</strong>ÔØØÓØÒ<strong>×</strong>α,<br />
ÒÓÓ<strong>×</strong><strong>×</strong><strong>×</strong><strong>×</strong>ÙØØØÃÐÐÒÓÖÑÒØØ<strong>×</strong><strong>×</strong><strong>×</strong>ÕÙÐØÓδ ÓÐÐÓÛÒÖØ<strong>×</strong>ÓÖg ]ØÐÖÓÄÙÖÒØÔÓÐÝÒÓÑÐ<strong>×</strong>ÒzºÌÒØÐÓÓÔÐÖ<strong>×</strong>ØÒÚÒÝ<br />
loop<br />
´¿º¼µ<br />
´¿º½µ<br />
ÌÒÒعÑÒ<strong>×</strong>ÓÒÐÐÓÓÔÐÖ¸<strong>×</strong>Ù<strong>×</strong>ÙÐÐÝÛÖØØÒÒØÓÐÐÓÛÒÛݺÄØL=<br />
ÒÓÛÒ<strong>×</strong>ØÖÚØÓÒÛ<strong>×</strong>ØÓÐÐÓÛÒÖØ<strong>×</strong>ÛØØÓØÖÒÖØÓÖ<strong>×</strong>¸℄ ÏÒØÓÓÒÑÓÖÒÖØÓÖ¸d¸ØÓØ<strong>×</strong>ÒØÖÐÐÝÜØÒÒÒعÑÒ<strong>×</strong>ÓÒÐÐÖ¸<br />
C[z, z −1 ´¿º¾µ<br />
´¿º¿µ<br />
[d, t α m ] = −[tα , d] = mt α m ; [d, k] = 0 .<br />
ÝØÑ<strong>×</strong>Ù<strong>×</strong>ØØÄÐÖgÒÓÛÒ<strong>×</strong>ØÓÖÞÓÒØÐ<strong>×</strong>ÙÐÖÓØÒÄ<br />
ÌÓÚÓÒ<strong>×</strong>ØÖÙØÓÒ<strong>×</strong>ØÒĝ<br />
ÐÖĝº 0ÚÚÒ<strong>×</strong>ÒÖØ<strong>×</strong>ÛØØÖÚØÓÒ¸ÒØ<strong>×</strong>ÙÐÖÒÖØ<br />
=<br />
ÌÒÖØÓÖ<strong>×</strong>t α <br />
[t α m, t β n] = f αβ γ t γ ⊗ z m+n − mkδ αβ δ m+n,0 ,<br />
[k, t α n] = 0 .<br />
g loop = L ⊗ C g = C[z, z −1 ] ⊗ C g.<br />
C[z, z −1 ] ⊗ C g. ⊕ Ck ⊕ Cd .<br />
αβ α
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