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

2000/01/30 by Yucai Su, Xiaoping Xu, Su, Yucai +3
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #math.QA

paper · pdf · doi:10.48550/arxiv.math/0001178

20pages, Latex file; To appear in Journal of Algebra

arxiv created 2000/01/30 · arxiv updated 2009/11/30

Abstract

We classify all the pairs of a commutative associative algebra with an identity element and its finite-dimensional commutative locally-finite 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 generalized simple Lie algebras of Cartan type. Moreover, we determine the isomorphic classes of the generalized simple Lie algebras of Witt Type. The structure space of these algebras is given explicitly.

Related

• Structure of Algebras of Weyl Type
• Structure of Divergence-Free Lie Algebras
• Lie algebras whose derivation algebras are simple
• Isomorphism classes and automorphism groups of algebras of Weyl type
• On finite-dimensional subalgebras of derivation Lie algebras