Simple algebras of Weyl type, II
Author:
Kaiming Zhao
Journal:
Proc. Amer. Math. Soc. 130 (2002), 13231332
MSC (2000):
Primary 16W10, 16W25, 17B20, 17B65, 17B05, 17B68
Published electronically:
October 25, 2001
MathSciNet review:
1879953
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Abstract: Over a field of any characteristic, for a commutative associative algebra , and for a commutative subalgebra of , the vector space which consists of polynomials of elements in with coefficients in and which is regarded as operators on forms naturally an associative algebra. It is proved that, as an associative algebra, is simple if and only if is simple. Suppose is simple. Then, (a) is a free left module; (b) as a Lie algebra, the subquotient is simple (except for one case), where is the center of . The structure of this subquotient is explicitly described. This extends the results obtained by Su and Zhao.
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Additional Information
Kaiming Zhao
Affiliation:
Institute of Mathematics, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing 100080, People’s Republic of China
Email:
kzhao@math08.math.ac.cn
DOI:
http://dx.doi.org/10.1090/S0002993901062189
PII:
S 00029939(01)062189
Keywords:
Simple Lie algebra,
simple associative algebra,
derivation
Received by editor(s):
August 28, 2000
Received by editor(s) in revised form:
November 20, 2000
Published electronically:
October 25, 2001
Additional Notes:
This work was supported by the Hundred Talents Program of Chinese Academy of Sciences and by NSF of China
Communicated by:
Lance W. Small
Article copyright:
© Copyright 2001
American Mathematical Society
