Commutative restricted Lie algebras

Commutative Restricted Lie Algebras1

Examples of such algebras are subspaces of associative algebras of characteristic p^O which are closed under the Lie multiplication [ab] =ab — ba and under pih powers. Then one may take a[pl =ap. It is known that every restricted Lie algebra is isomorphic to one of this type. For this reason we may simplify our notation in the sequel and write a" for alp]. We call the mapping a—>ap the p-operat...

Commutative Restricted Lie Algebras1

Examples of such algebras are subspaces of associative algebras of characteristic p^O which are closed under the Lie multiplication [ab] =ab — ba and under pih powers. Then one may take a[pl =ap. It is known that every restricted Lie algebra is isomorphic to one of this type. For this reason we may simplify our notation in the sequel and write a" for alp]. We call the mapping a—>ap the p-operat...

Restricted Lie Algebras

Cohomology of Restricted Lie Algebras

In this dissertation, we investigate the cohomology theory of restricted Lie algebras. Motivations for the definition of a restricted Lie algebra are given and the theory of ordinary Lie algebra cohomology is briefly reviewed, including a discussion on algebraic interpretations of the low dimensional cohomology spaces of ordinary Lie algebras. The general Cartan-Eilenberg construction of the st...

Part Iv.1. Lie Algebras and Co-commutative Co-algebras

Introduction 2 1. Lie algebras: recollections 3 1.1. The basics 3 1.2. Scaling the structure 3 1.3. Filtrations 4 1.4. The Chevalley complex 4 1.5. The functor of primitives 6 1.6. The enhanced adjunction 6 1.7. The symmetric Hopf algebra 8 2. Looping Lie algebras 9 2.1. Group-Lie algebras 10 2.2. Forgetting to group structure 10 2.3. Chevalley complex of group-Lie algebras 11 2.4. Chevalley co...