УК гд а Уж × в
УК гд а Уж × в
УК гд а Уж × в
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Q¸ÒØÒÖÐ<strong>×</strong>¸ÑÝÒÓØÒÒØÖÐÐØظ<strong>×</strong>ÒÒÒÖÐØÒÜÒ<strong>×</strong>Ø ÔØÖ¿ºÃÅÄÐÖ<strong>×</strong><br />
<strong>×</strong>Ô<strong>×</strong>ÒÝØÓÚÖÓÓØÚØÓÖ<strong>×</strong>º<br />
I<strong>×</strong>ÓÙÒØÐÝÒÒØÒÛ<strong>×</strong>ØÖÒÓQ<strong>×</strong>ÒÓØÒغÆÓÛÛÓÑØÓØÖÓÓØ<br />
−αµ<strong>×</strong>Ø<strong>×</strong>Ù<strong>×</strong>ÔÓ ÒØÓÒ¿ººÓÖα =<br />
α<strong>×</strong>ÐÐØÑÙÐØÔÐØÝÓØÖÓÓØαº α<strong>×</strong>ÒÓÒ¹ØÖÚкÌ<br />
k=1i k ∈ Q¸ØÖÓÓØ<strong>×</strong>ÔG α´Ö<strong>×</strong>ÔºG GÒÖØÝØÐÑÒØ<strong>×</strong>[e ij [. . .[e i2 , e ]]]´Ö<strong>×</strong>Ôº[f i1 [. . .[f i2 , f ]]]µºÒÓÒ¹ÞÖÓÐÑÒØα<br />
i1<br />
ÓØÓÖÑÐÖÓÓØÐØØQ<strong>×</strong><strong>×</strong>ØÓÖÓÓØÓGØ<strong>×</strong>Ù<strong>×</strong>ÔG ÑÒ<strong>×</strong>ÓÒÓØÖÓÓØ<strong>×</strong>ÔG −αiÓÖØ<strong>×</strong>ÑÔÐÖÓÓØ<strong>×</strong>ÖÓÒ¹ÑÒ<strong>×</strong>ÓÒкÐ<strong>×</strong>Ó¸<strong>×</strong>ÓÖÐÐØÖÓÓØ<strong>×</strong>α∈QÒ αiÒ ÌÓÙÒÖ<strong>×</strong>ØÒØ<strong>×</strong>¸ÓÑÔÖÛØØÐ<strong>×</strong>ØÖÐØÓÒÒ´¿º¿µºÐÐØÖÓÓØ<strong>×</strong>Ô<strong>×</strong>ÓÖi∈I ÖÚÒ<strong>×</strong>G ÒØÓÒ¿ºº = Ce<br />
1ÓGºÌÖ<strong>×</strong>Ð<strong>×</strong>ÓØÓÒÔØÓÔÓ<strong>×</strong>ØÚÒÒØÚÖÓÓغ<br />
α<strong>×</strong>ØÖÓÒØÒÒØÚÒÔÖØ<br />
iÒG = Cf iºÁÒÔÖØÙÐÖ¸Ò<strong>×</strong>ÓÖ¸ØÖÓÓØ<strong>×</strong>Ô<strong>×</strong>G GÜÔÖ<strong>×</strong><strong>×</strong><strong>×</strong><strong>×</strong>ÙÑÓ<strong>×</strong>ÑÔÐÖÓÓØ<strong>×</strong>ºÌÖÓÓØ<strong>×</strong>ÔG G 0ÓÖØÓÔÖØG <strong>×</strong><strong>×</strong>ÙÑÓ<strong>×</strong>ÑÔÐÖÓÓØ<strong>×</strong>º a<strong>×</strong><strong>×</strong>ØÓÔÓ<strong>×</strong>ØÚ´Ö<strong>×</strong>ÔºÒØÚµα´Ö<strong>×</strong>Ôº−αµ<br />
1µº<br />
½ºÖÓÓØ= 0}Ò<strong>×</strong>ÛÖØØÒ<strong>×</strong>ÙÔÔ(α)º<br />
¾ºÖÓÓØα<strong>×</strong><strong>×</strong>ØÓÚÒ´Ö<strong>×</strong>ÔºÓµG α ≤ G 0´Ö<strong>×</strong>ÔºG kiÒ<strong>×</strong>ÛÖØØÒØ(α)º<br />
1µºÏØÒÛÖØd(α) =<br />
´Ö<strong>×</strong>Ôºd(α) =<br />
¿ºÌØÓÖÓÓØα = ∑ i<strong>×</strong>ÒØÓ∑ k i<br />
α<br />
ÏÖÓÒÞØÓÚ<strong>×</strong>ØØÑÒØ<strong>×</strong>ÒØÓÒØÜØÓÒعÑÒ<strong>×</strong>ÓÒÐ<strong>×</strong>ѹ<strong>×</strong>ÑÔÐÄй Ö<strong>×</strong>¸ÙØÔÒÒÑÒØØÒÓÛÛÐ<strong>×</strong>ÓÚÑÒÖÝ<strong>×</strong>ÑÔÐÖÓÓØ<strong>×</strong>ÒØÐÖº<br />
ºÌ<strong>×</strong>ÙÔÔÓÖØÓα<strong>×</strong>Ø<strong>×</strong>Ø{i ∈ I : k i ≠<br />
ÓÖÒÝÖÓÓØα∈Lº¸ÑÙÐØ(α)ÑÙÐØ(−α)¸ÒÖÓÓØα<strong>×</strong>ÔÓ<strong>×</strong>ØÚÒÓÒÐÝØÖÓÓØ<br />
º<strong>×</strong>ÓØ<strong>×</strong>ØÓÖÓÓØ<strong>×</strong>L<strong>×</strong>ÐÒÖÐÝÒÔÒÒØ<strong>×</strong>Ù<strong>×</strong>ØΠ<strong>×</strong>ÙØØÓÖÒÝα∈<br />
L, α = ∑ β∈Π k ββ¸ÛÖÓÖÐÐβ∈ Π¸ØÖÐÐØ<strong>×</strong>ÐÖ<strong>×</strong>k β ∈ Z<br />
ØÖØÒÓÑÔÓ<strong>×</strong>ÓÒØÃÅÄ<strong>×</strong>ÙÔÖÐÖG<strong>×</strong>ÖØ<strong>×</strong>ÙÑÓÖÓÓØ<strong>×</strong>Ô<strong>×</strong><strong>×</strong><br />
−α<strong>×</strong>ÒØÚºÌ<strong>×</strong>Ú<strong>×</strong>Ù<strong>×</strong>ÓÑÔÓ<strong>×</strong>ØÓÒÓØ<strong>×</strong>ØÓÖÓÓØ<strong>×</strong>ÒØÓÔÓ<strong>×</strong>ØÚÒÒØÚ<br />
−º<strong>×</strong>ÓÖ¸Ø<strong>×</strong>ÐÐÓÛ<strong>×</strong>Ù<strong>×</strong>ØÓÖÐÞ<br />
+ÓÖÐÐk ÓÒ<strong>×</strong>ºÌ<strong>×</strong>ØÓÖÓÓØ<strong>×</strong>LÓÑÔÓ<strong>×</strong><strong>×</strong>ÒØÓL = L +<br />
´¿º¿µ<br />
∪ L<br />
h)xºÌÒ¸ÓÖ ÄØα ∈ LÒh α ∈ H<strong>×</strong>ÙØØÓÖÐÐx G αÒh Mh¸[h, x] = (h α<br />
<br />
,<br />
ÐÐy∈ G<br />
∑ j<br />
−αi<br />
ij<br />
αº<br />
G = (⊕ α∈L+ )G α ⊕ H ⊕ (⊕ α∈L− G α ) .<br />
∈ ∈<br />
−α¸[x, y] = (x, y)h<br />
β<br />
−º<br />
0<br />
∈ Z
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