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Simple algebras of Weyl type

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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.

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Authors and Affiliations

  1. Department of Applied Mathematics, Shanghai Jiaotong University, 200030, Shanghai, China

    Yucai Su

  2. Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, 100080, Beijing, China

    Kaiming Zhao

Authors
  1. Yucai Su
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  2. Kaiming Zhao
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Correspondence to Yucai Su.

Additional information

Su, Y., Zhao, K., Second cohornology group of generalized Witt type Lie algebras and certain representations, submitted to publication

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Su, Y., Zhao, K. Simple algebras of Weyl type. Sci. China Ser. A-Math. 44, 419–426 (2001). https://doi.org/10.1007/BF02881878

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  • DOI: https://doi.org/10.1007/BF02881878

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