Simple algebras of Weyl type |
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Authors: | SU Yucai ZHAO Kaiming |
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Affiliation: | 1. Department of Applied Mathematics, Shanghai Jiaotong University, 2. Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, |
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Abstract: | Over a fieldF of arbitrary characteristic, we define the associative and the Lie algebras of Weyl type on the same vector spaceA[D] =A⊗F[D] from any pair of a commutative associative algebra,A with an identity element and the polynomial algebraF[D] of a commutative derivation subalgebraD ofA We prove thatA[D], as a Lie algebra (modulo its center) or as an associative algebra, is simple if and only ifA isD-simple andA[D] acts faithfully onA. Thus we obtain a lot of simple algebras. Su, Y., Zhao, K., Second cohornology group of generalized Witt type Lie algebras and certain representations, submitted to publication |
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Keywords: | simple Lie algebra simple associative algebra derivation |
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