外代数上线性模非线性扩张问题.doc

10530


200709010827
Non-linear Extension of Linear Modules
over Exterior Algebras
Candidate
Supervisor and Rank

Jiao Fu
Prof. Jinyun Guo
College
Program
Specialization
Degree
University
Date

Mathematics putational Science
Pure Mathematics
Representation Theory of Algebras
Master of Science
Xiangtan University
June 1th, 2010
........................................................I
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II
1
2
3
4
5

.............................................1
. ........................................7
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
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V

,
.
,

.
,
 a

 b a
... ...

. . .

. .
c b a










n×n









a
b
0
.
0
0

.
0 ···


a 
b a 
.. 
0 ··· ··· b 

(m+1)×m
c

,
1
1

2

2
n

m
(a, b, c)
m
(a, b, c)
(a, b)
t−
(a, b)
t−

s−
,
t

.
1
n
(a, b, c)
t−
.
.
,
s−
.


.


1


(a, b, c)
t−

2
m
(a, b)
1
n
(a, b, c)
t−
.
:

,

,

,

,
I
 b a






.. ..
 c


.. .. ..














, 



..





.. ... ...


. a 

Abstract
Exterior algebras, which are defined in a vector space V , are a class of very
important algebra. Exterior algebras and their modules, with strong application
background. There is a series of study on exterior algebras and their modules re-
cently, howeve