# Simple Lie algebras over fields of positive characteristic. I, Structure theory [electronic resource] / by Helmut Strade.

##### By: Strade, Helmut.

Material type: TextSeries: De Gruyter expositions in mathematics: 38.Publisher: New York : Walter de Gruyter, 2004Description: 1 online resource (viii, 540 p.) : ill.ISBN: 9783110197945 (electronic bk.); 3110197944 (electronic bk.).Other title: Structure theory.Subject(s): Lie algebras | MATHEMATICS -- Algebra -- LinearGenre/Form: Electronic books.Additional physical formats: Print version:: Simple Lie algebras over fields of positive characteristic. I, Structure theory.DDC classification: 512/.55 Online resources: EBSCOhostIncludes bibliographical references (p. [527]-537) and index.

Simple Lie Algebras over Fieldsof Positive Characteristic; Contents; Introduction; Chapter 1Toral subalgebras in p-envelopes; Chapter 2Lie algebras of special derivations; Chapter 3Derivation simple algebras and modules; Chapter 4Simple Lie algebras; Chapter 5Recognition theorems; Chapter 6The isomorphism problem; Chapter 7Structure of simple Lie algebras; Chapter 8Pairings of induced modules; Chapter 9Toral rank 1 Lie algebras; Notation; Bibliography; Index.

The problem of classifying the finite-dimensional simple Lie algebras over fields of characteristic p & 0 is a long-standing one. Work on this question during the last 35 years has been directed by the Kostrikin-Shafarevich Conjecture of 1966, which states that over an algebraically closed field of characteristic p & 5 a finite-dimensional restricted simple Lie algebra is classical or of Cartan type.

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#### Other editions of this work

Simple Lie algebras over fields of positive characteristic. by Strade, Helmut, ©2009 | |

Simple Lie algebras over fields of positive characteristic. by Strade, Helmut, ©2009 | |

Simple Lie algebras over fields of positive characteristic. by Strade, Helmut, ©2009 |

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