УК гд а Уж × в
УК гд а Уж × в
УК гд а Уж × в
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ÔØÖ¿ºÃÅÄÐÖ<strong>×</strong><br />
¿ºº½ ¿º ÖÁÒØÖÓÙØÓÒØÓÃÅÄ<strong>×</strong>ÙÔÖÐÖ<strong>×</strong><br />
ÄØÙ<strong>×</strong><strong>×</strong>ØÖØÛØØÒÓØÓÒÓ<strong>×</strong>ÙÔÖÚØÓÖ<strong>×</strong>Ôº<strong>×</strong>ÙÔÖÚØÓÖ<strong>×</strong>Ô<strong>×</strong>ÚØÓÖ ËÙÔÖÐÖ<strong>×</strong> 2¹Ö¸ºº<strong>×</strong>ØÓÑÔÓ<strong>×</strong>ØÓÒ<br />
ÒÒÒÖÐÒM¹ÖÚØÓÖ<strong>×</strong>Ô<strong>×</strong>ØÓÑÔÓ<strong>×</strong>ØÓÒ ´¿ºµ <strong>×</strong>ÔÓÚÖÐØØ<strong>×</strong>Z α<strong>×</strong><strong>×</strong>ØÓÓÑÓÒÓÙ<strong>×</strong>ÓÖαºÓÖÚØÓÖ<strong>×</strong>ÔV¸Ø<strong>×</strong><br />
V = V 0 ⊕ V 1 , 0, 1 ∈ Z 2<br />
´¿ºµ<br />
= Z/2Z ,<br />
V = ⊕ V α .<br />
α∈M<br />
ÒÐÑÒØÓV α+βºÌÖÒÒÑÓÖÒÖÐ<strong>×</strong>ÓÚÓÖÚØÓÖ<strong>×</strong>Ô<strong>×</strong>¸ÙØÛÛÐÐ<br />
VÖÜÑÔÐ<strong>×</strong><br />
)¸ÒØÜØÖÓÖÐÖ∧ ØÒ<strong>×</strong>ÓÖÐÖT(V )¸<strong>×</strong>ÝÑÑØÖÐÖS(V 2¹ÖÒ<strong>×</strong>º<br />
1¸ÓÖÛ<br />
ÙØÒÓÛÓÒ<strong>×</strong>ØÓÔÒÑÒØÓÒ<strong>×</strong><strong>×</strong>ØÒÝÑÔÓ<strong>×</strong>ÝØÖÒº <strong>×</strong>Ù¹ÐÖÓ<strong>×</strong>ÙÔÖÐÖ<strong>×</strong>Ð<strong>×</strong>Ó<strong>×</strong>ÙÔÖÐÖ¸Ò<strong>×</strong>Ù¹<strong>×</strong>ÙÔÖÐÖIÓg<strong>×</strong><br />
ÓÖÚØÓÖ<strong>×</strong>Ô<strong>×</strong>º<strong>×</strong>ÙÔÖÐÖ<strong>×</strong>Z 2¹ÖÐÖ¸A=A 0 ⊕ A<br />
A α A β<br />
IºÄ<strong>×</strong>ÙÔÖÐÖ<strong>×</strong>Ò<strong>×</strong>ÑÐÖØÓÖÙÐÖÄÐÖ¸<br />
⊆ A<br />
ÑÒÐÝÓÒ<strong>×</strong>ÖÒZ <strong>×</strong>Ø<strong>×</strong>ÝÒ<br />
ÐÐÒÐ[I, g] ⊆<br />
1ÛØÄÖØ ÒØÓÒ¿ºº½Ä<strong>×</strong>ÙÔÖÐÖ<strong>×</strong>Z 2ÖÐÖg = g 0 ⊕ g<br />
´¿º¼µ<br />
[x,<br />
Ä<strong>×</strong>ÙÔÖÐÖ<strong>×</strong>ÒÓØÄÐÖØÛÝÓÒÙÒÖ<strong>×</strong>ØÒ<strong>×</strong><strong>×</strong>ѹ<strong>×</strong>ÑÔÐÄÐÖ<strong>×</strong>º ÖÐÐØÚÒÒÓÔÖØ<strong>×</strong>Ógº<br />
z]] = [[x, y]z] + (−1) d(x)d(y) [[x, z]y] ,<br />
ÛÖÓÖÒÝÓÑÓÒÓÙ<strong>×</strong>ÐÑÒØg∈ g n , n<br />
0ÑÓÙкÓÒ<strong>×</strong>ÖØ<strong>×</strong><strong>×</strong>ÓØÚÐÖ<br />
= 0, 1,(g) = nºÌ<strong>×</strong>Ù<strong>×</strong>Ô<strong>×</strong>g 0Òg 1<br />
g 0<strong>×</strong>ÒÓÖÒÖÝÄÐÖ¸ÛÐg 1<strong>×</strong>g <br />
Ò<br />
[x[y,<br />
y] = −(−1)(x)(y) [y, x] ´¿ºµ
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