Mathematical Sciences: Nonassociative Algebras

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This project is concerned with research on simple Lie algebras of prime characteristic. The principal investigators have made significant progress in analyzing the structure of 1-sections of simple algebras and have begun studying 2-sections. The determination of the 1- and 2-sections was an essential step in the classification of the restricted simple Lie algebras and it is believed to be an essential step in the classification of the nonrestricted algebras as well. The principal investigators will do an extensive investigation of the structure of 2-sections in simple prime characteristic algebras and will apply the information obtained to the classification of the simple nonrestricted Lie algebras. Work will also be done on bringing over certain stability results to the affine Kac-Moody setting. The characterization of finite dimensional Lie algebras over an algebraically closed field of prime characteristic has a long history and is one of the important outstanding problems in mathematics. This project supports work on the remaining cases of this characterization.