Isomorphisms of Steinberg groups over commutative rings |
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| Authors: | Li Fuan |
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| Institution: | (1) Institute of Mathematics, Academia Sinica, China |
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| Abstract: | LetA andR be commutative rings, andm andn be integers 3. It is proved that, if  :St
m (A) St
n (R) is an isomorphism, thenm=n. Whenn4, we have: (1) Every isomorphism :St
n(A)St
n(R) induces an isomorphism :E
n (A)E
n (R), and is uniquely determined by; (2) IfSt
n (A)  St
n (R) thenK
2.n
(A)K
2.n
(R); (3) Every isomorphismE
n (A) E
n (R) can be lifted to an isomorphismSt
n(A)St
n(R); (4)St
n(A) St
n(R) if and only ifAR. For the casen=3, ifSt
3(A) andSt
3(R) are respectively central extensions ofE
3(A) andE
3 (R), then the above (1) and (2) hold.The Project supported by National Natural Science Foundation of China |
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| Keywords: | |
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