Simple algebras of Weyl type, II

Author:
Kaiming Zhao

Journal:
Proc. Amer. Math. Soc. **130** (2002), 1323-1332

MSC (2000):
Primary 16W10, 16W25, 17B20, 17B65, 17B05, 17B68

DOI:
https://doi.org/10.1090/S0002-9939-01-06218-9

Published electronically:
October 25, 2001

MathSciNet review:
1879953

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Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0002-9939-01-06218-9

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