外代数上线性模的二次线性扩张问题.pdf

《外代数上线性模的二次线性扩张问题.pdf》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。

1、Æ“Ò10530ÆÒ200909010996©aÒO153.3—?a¬ÆØ©“êþ‚5g‚5*ܯKÆž<Üù•“HAÇƶ¡êƆOŽ‰ÆÆƉ;’Ä:êÆïÄ••“êL«Ø"˜co›F“êþ‚5g*ܯKÆž<Üù“6¶9…¡HAÇƶ¡êƆOŽ‰ÆÆƉ;’Ä:êÆïÄ••“êL«ØÆž?OnÆa¬Æǃü‰ŒÆØ©JFÏ"˜co›FIteratedLinearExtensionofLinearModulesoverExteriorAlgbrasCandidat

2、eZhangHongSupervisorandRankProf.JinyunGuoCollegeMathematicsandComputationalScienceProgramFundamentalMathematicsSpecializationRepresentationTheoryofAlgebrasDegreeMasterofScienceUniversityXiangtanUniversityDateApril20th,2012‰ŒÆÆØ©M5(²

3、ïĤJ"Ø©¥AO±I5Ú^SN§ةع?ÛÙ¦‡<½8N®²uL½>L¤JŠ¬"é©ïĉѕ‡z‡<Ú8N§þ®3©¥±²(•ªI²"<¿£(²{ÆJd<«ú"Šö¶µFϵcFÆØ©‡¦^ÇÖÆØ©Šö)Æk'3!¦^ÆØ©5½§Ó¿Æ3¿•I[k'Ü€½ÅxØ©E<‡Ú>f‡§#NØ©Ú/"<ljŒÆŒ±òÆØ©ܽܩSN?k'êâ¥?1u¢§Œ±æ^K

4、FϵcF“¶µFϵcFÁ‡V´“ê4•kþ•þ˜m,a;b´V¥‚5Ã'ƒ,^V´Vþ“ê.òL«ÝäkXe/ª^V-M‰Ì‚•Ý•mE,Ý•24‚5.01aBCBCBbaCFm(a;b)=BBCC....B..aC@A...b(m+1)m©b½V´kþ3‘•þ˜m,a;b;c´V¥‚5Ã'ƒ,·‚?Øn‡‚5^V-M;L;I*ܯK.M;L;IL«Ý©O•F1(a;b);F1(a;c);F1(b;c),N´M/Ïumnpft(J)L‚5*Ü,J´N/ÏuI‚5*Ü.Ü

5、


!Pt(J)!


!f1(J)f0(J)P1(J)!P0(J)!J!0´J4Ý©).Œ·ÀPt(J)Ä,¦ft(J)Ýäk01Ft(a;b)00BmCFt(J)=BBttCCCFn(a;c)0@ADtDtFt(b;c)12p/ª,…Ct•[21]¤(½,©?ØL«ÝF1(J).·‚y²:½n3.2M;L;I•^V‚5,KŒ·ÀPi(J),i2Ä,¦010


0w1cB1;mCB......1C1BB...w2;mcCCD1=BC;B0


0w1cC@p;mAv1b


v1bw1

6、cp+1;1p+1;mp+1;m(p+1)m010


00w2cB1;mCB..........CB.....CD2=BC;1BCB0


00w2cC@p+1;mAv2b


v2bv2bw2cp+2;1p+2;m1p+2;mp+2;m+1(p+2)(m+1)I01010


000


00BCBCB........CB........CB....CB....CD1=BC;D2=BC:2BC2BCB0


00CB0


00C@A@A00


0y1b00


0y1bp+1;np+2;n+1(p+1)n(p+2)

7、(n+1)31oÙ‰Ñü‡ùS“*ÜÓ^‡.'…c:“ê;‚5;‚5*Ü;L«Ý;ÓÝIIAbstractLetVbealinearspaceoveralgebraicclosedeldk,a;bbelinearindepen-dentvectorsinV.^VistheexterioralgebraoverV.Linearmoduleissaidtobeminimallinearmoduleswithcycliclengthmandcomplexitytwoiftheirrepresentationmatrix

8、havethefollowingform:01aBCBCBbaCFm(a;b)=BB....CC:B..aC@A...b(m+1)mInthispaper,letVbean3-dimensionallinearspaceoverk.a;b;cbe