Leibniz Algebras: Structure and Classification

ISBN-13: 9780367354817 / Angielski / Twarda / 2019 / 303 str.

Shavkat Ayupov; Bakhrom Omirov; Isamiddin Rakhimov

Opis

Leibniz Algebras: Structure and Classification is designed to introduce the reader to the theory of Leibniz algebras.

Leibniz algebra is generalization of Lie algebras. These algebras preserve a unique property of Lie algebras that the right multiplication operators are derivations.

Spis treści

1. INTRODUCTION.  1.1. ALGEBRAS.  1.2. ASSOCIATIVE ALGEBRAS.  1.3. LIE ALGEBRAS.  1.4. LODAY ALGEBRAS.  2. STRUCTURE OF LEIBNIZ ALGEBRAS.  2.1. SOME PROPERTIES OF LEIBNIZ ALGEBRAS.  2.2. NILPOTENT AND SOLVABLE LEIBNIZ ALGEBRAS.  2.3. ON LEVI’S THEOREM FOR LEIBNIZ ALGEBRAS.  2.4. SEMISIMPLE LEIBNIZ ALGEBRAS.  3. CLASSIFICATION PROBLEM IN LOW DIMENSIONS.  3.1. ALGEBRAIC CLASSIFICATION OF LOW-DIMENSIONAL.  LEIBNIZ ALGEBRAS.  3.2. APPLICATION.  3.3. LOW-DIMENSIONAL NILPOTENT LEIBNIZ  ALGEBRAS.  3.4. 4-DIMENSIONAL SOLVABLE LEIBNIZ ALGEBRAS.  3.5. RIGIDITY OF LIE AND LEIBNIZ ALGEBRAS.  3.6. LEIBNIZ COHOMOLOGY COMPUTATIONS.  3.7. A RIGID LEIBNIZ ALGEBRA WITH NON-TRIVIAL HL^2.  3.8. LIE-RIGIDITY VERSUS LEIBNIZ-RIGIDITY.  4. ON SOME CLASSES OF LEIBNIZ ALGEBRAS.  5. ISOMORPHISM CRITERIA FOR FILIFORM LEIBNIZ ALGEBRAS.  5.1. ON BASE CHANGES IN COMPLEX FILIFORM LEIBNIZ ALGEBRAS.  5.2. A CRITERION OF ISOMORPHISMS OF COMPLEX FILIFORM.  NON-LIE LEIBNIZ ALGEBRAS.
6. CLASSIFICATION OF FILIFORM LEIBNIZ ALGEBRAS IN LOW DIMENSIONS.  6.1. ISOMORPHISM CRITERIA FOR THE FIRST CLASS.  6.2. CLASSIFICATION OF THE FIRST CLASS IN LOW DIMENSIONS.  6.3. ISOMORPHISM CRITERIA FOR THE SECOND CLASS.  6.4. CLASSIFICATION OF THE SECOND CLASS IN LOW DIMENSIONS.  6.5. SIMPLIFICATIONS AND NOTATIONS IN THE THIRD CLASS.  6.6. CLASSIFICATION IN DIMENSION FIVE.  6.7 CLASSIFICATION IN DIMENSION SIX.