УК гд а Уж × в
УК гд а Уж × в
УК гд а Уж × в
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ÒØÖÐÐÑÒظ<strong>×</strong>ÛÛÐÐ<strong>×</strong>¸<strong>×</strong>ØÙÖØØÛÛÐÐÒÒÐÐÒÒعÑÒ<strong>×</strong>ÓÒÐ ÔØÖ¿ºÃÅÄÐÖ<strong>×</strong><br />
ÒÑÔÓ<strong>×</strong>Ò ÄÐÖ<strong>×</strong>ºÚÒÒعÑÒ<strong>×</strong>ÓÒÐÄÐÖg¸ÛÒØÖÝÒÓÒ<strong>×</strong>ØÖÙØÒ´l¹<br />
i¸ØÓØÐÖ<br />
<strong>×</strong>ÓÐÐÓÛ<strong>×</strong> Ì<strong>×</strong>ÛÐÐÑÓÝØÖØ<strong>×</strong>ØÛÒØÓÖÒÐÒÖØÓÖ<strong>×</strong>ØÓÒÐÙØÒØÖÐÒÖØÓÖ<strong>×</strong><br />
ÑÒ<strong>×</strong>ÓÒеÒØÖÐÜØÒ<strong>×</strong>ÓÒØÓØÝ<strong>×</strong>ÑÔÐÝÒlÒØÖÐÒÖØÓÖ<strong>×</strong>¸k [t α , k i ] = 0ÓÖi<br />
ØÂÓÒØØÝÒØÙ<strong>×</strong>ÒÒÓØÓÑÔÐØÐÝÖØÖÖݺÌÒÙÑÖÓ<strong>×</strong>ÓÐÙØÓÒ<strong>×</strong>ØÓ ´¿ºµ<br />
ØÓÚÕÙØÓÒ<strong>×</strong>ÙØØÓØÂÓÒØØÝÓÒ<strong>×</strong>ØÖÒØ<strong>×</strong>ØÒÙÑÖÓÒÔÒÒØ<br />
iÚØÓ<strong>×</strong>Ø<strong>×</strong>Ý<br />
[t α , t β ] = f αβ γ tγ + f αβ i ki ,<br />
ÛÖf<br />
<strong>×</strong>ÓÐÙØÓÒºÀÒ¸ØÒØÖÓÒعÑÒ<strong>×</strong>ÓÒÐ<strong>×</strong>ѹ<strong>×</strong>ÑÔÐÄÐÖ<strong>×</strong>ØÖÚкÌÙ<strong>×</strong>¸<br />
iÖÓÑØÓÚÕÙØÓÒ<strong>×</strong>ÓÛ<strong>×</strong>¸<br />
αβ<br />
γÖØ<strong>×</strong>ØÖÙØÙÖÓÒ<strong>×</strong>ØÒ<strong>×</strong>ÓgºÌÒÛ<strong>×</strong>ØÖÙØÙÖÓÒ<strong>×</strong>ØÒØ<strong>×</strong>f αβ<br />
ØÓÒØÖÐÐÝÜØÒØÄÐÖg¸ÛÒØÓÐØÖØ<strong>×</strong><strong>×</strong>ØÖÙØÙÖØÓÐÐÓÛÓÖØÜØÒ<strong>×</strong>ÓÒº<br />
0<strong>×</strong>ØÓÒÐÝÔÓ<strong>×</strong><strong>×</strong>Ð<br />
Ì<strong>×</strong>Ð<strong>×</strong>ØÓØÓØÐÓÓÔÐÖÓÒعÑÒ<strong>×</strong>ÓÒÐÄÐÖº<br />
ÒØÖÐÜØÒ<strong>×</strong>ÓÒ<strong>×</strong>ÓÒÒÛÖØÓÛÒÓÖgºÒÒØk ÄØg<strong>×</strong>ÑÔÐÄÐÖ¸ÒÓÒ<strong>×</strong>ÖØ<strong>×</strong>ÔÓÒÐÝØÑÔ<strong>×</strong>ÖÓÑØÖÐ<br />
ÓÖÒعÑÒ<strong>×</strong>ÓÒÐÄÐÖ<strong>×</strong>¸ØØØØÖÚÐ<strong>×</strong>ÓÐÙØÓÒf αβ<br />
i =<br />
ÓÑÔÐÜÔÐÒÛØÓÓÖÒØzºÌÒ<strong>×</strong><strong>×</strong>ÓÖØÓÚÚØÓÖ<strong>×</strong>ÔÓÒÐÝØÑÔ<strong>×</strong> ÒÖØ<strong>×</strong>ÒØÙÖÐÖØÓÔÖØÓÒÖÓÑØÄÐÖg<strong>×</strong><br />
1ØÙÒØÖÐÒØ<br />
S 1ØÓgº<strong>×</strong>ÓÖ¸ÐØ{t |α = 1, . . .,r}<strong>×</strong><strong>×</strong>Óg¸ÒS ÖÓÑS ÒØÙ<strong>×</strong>¸ nºÌ<strong>×</strong><strong>×</strong>Ô ´¿ºµ<br />
1ØÓgÛÐÐÓØÓÖÑ{tα n Z}¸ÛÖt n = tα ⊗ z<br />
γÖ<strong>×</strong>ØÖÙØÙÖÓÒ<strong>×</strong>ØÒØ<strong>×</strong>ÓgºÏØØÓÚÖØØ<strong>×</strong><strong>×</strong>ÔÓÑ<strong>×</strong>Ä ´¿ºµ<br />
[t α m , tβ n ] ≡ [tα ⊗ z m , t β ⊗ z n ] = [t α , t β ] ⊗ (z m · z n ),<br />
ÒÙÑÖÓÒÖØÓÖ<strong>×</strong>º<br />
[t α m, t β n] = f αβ γ t γ ⊗ z m+n = f αβ γ t γ m+n,<br />
ÛÖf αβ loop<strong>×</strong>ÒÒÒØ<br />
loopÒÖØ ÐÖÐÐØÐÓÓÔÐÖ¸ÒÓØg loopºÆÓØØØØ<strong>×</strong>ÙÐÖÓg ÝØÒÖØÓÖ<strong>×</strong>tα loopÒØ<strong>×</strong>ÑÛÝ<strong>×</strong>ÛÓÖgºÏ 0<strong>×</strong>Ù<strong>×</strong>ØØ<strong>×</strong>ÙÐÖgºÆÓØØظØÐÖg ÆÓÛ¸ÛÒÐÓÓÓÖÒØÖÐÜØÒ<strong>×</strong>ÓÒØÓg <br />
α<br />
´¿ºµ<br />
= 1, . . ., l, α = 1, . . .,r .<br />
|α = 1, . . ., r; n ∈<br />
α
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