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Derivation-Simple Algebras and the Structures of Lie Algebras of Witt Type

✍ Scribed by Yucai Su; Xiaoping Xu; Hechun Zhang

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 146 KB
Volume: 233
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.2000.8442

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✦ Synopsis

We classify all the pairs of a commutative associative algebra with an identity element and its finite-dimensional locally finite Abelian derivation subalgebra such that the commutative associative algebra is derivation-simple with respect to the derivation subalgebra over an algebraically closed field with characteristic 0. Such pairs are the fundamental ingredients for constructing simple Lie algebras of Cartan type. Moreover, we determine the isomorphism classes of the simple Lie algebras of Witt type. The structure space of these algebras is given explicitly.

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