Invariantes de Forma de las Texturas Vía s3

7/24/2019 Invariantes de Forma de las Texturas Va s3

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3.


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4/20

1016

Mu

Md Ml


5/20


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x S

x S

S

P(x) x x|P(x)

N

Q

R


7/20

bien definidos

R

S

S S

R S

aRa a S

aRb bRa

aRb bRa aRc

R

S

S

a y S yRa a S

R S

S S

S


8/20

S

SS

x y= y x x, y S

(x y) z= x(y z)

x,y,z S

e S

e x= x e= x x S

x, y S x y= y x= e

{a,b,c}


9/20

G,

G1 a (b c) = (a b) c a,b,c G

G2 eG e x= x e x G

G3 a G a

a a =a a= e

e

=

{e, a}


10/20

{e, a}

a a

G= {e,a,b}


11/20

{1, 2, 3}

1, 2, 3, 1, 3, 2, 2, 1, 3, 2, 3, 1, 3, 1, 2

3, 2, 1

: A B

: A B

B = C = A


12/20

A= Sa

Sa

{1, 2,3, . . . , n}

A n Sn

Sn n!

S3 3! = 6

A= {1, 2, 3}

0=

1 2 3

1 2 3

, 1=

1 2 3

2 3 1

, 2=

1 2 3

3 1 2

,

1=

1 2 3

1 3 2

, 2=

1 2 3

3 2 1

, 3=

1 2 3

2 1 3

.


13/20

{1, 2, 3}

n n

n!

S3

S3 i)

ii)


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0=

1 0 00 1 00 0 1

1=0 1 00 0 1

1 0 0

2=0 0 11 0 0

0 1 0

1=

1 0 0

0 0 1

0 1 0

2=

0 0 1

0 1 0

1 0 0

3=

0 1 0

1 0 0

0 0 1

A,B,C n n C C1

CC1 = C1 = I A = C B C1

{A, B} ARB

S

A= C A C1 C= I ARA

A= C BC1


15/20

=C1 A C= (C1 C)B(C C1)

=C1 A C=B

ARB BRA

A= C BC1 A= DBD1

=DED1

=C BC1

DED1 C=C B

(C1 D)E(D1 C) =B

D1 C=C1 D1

=B

1 D)EC1 D1

=B

= C1 D

E 1 =B

ARB ARE BRE


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W Z0


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VCKM

VCKM

u =

0 Cu 0

Cu Bu Bu

0 Bu Au

, Md=

0 Cd 0

Cd Bd Bd

0 Bd Ad


18/20

Mu1

=1

Mu1T

=

0 0 Cu

0 Au BuCu Bu Bu

2u =2Mu2

T =

Au Bu 0

Bu Bu Cu

0 Cu 0

1u =1Mu1

T =

Bu Bu Cu

Bu Au 0

C 0 0

2u =2Mu2

T =

Bu Cu CuCu 0 0Bu 0 Au


19/20

VCKM


20/20

Invariantes de Forma de las Texturas Vía s3

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