Please let me know if you find any mistakes! Friday, October 3, 2014. Grading will be based on an exam on Friday, December 12. Groups of general interest often have some additional natural structure: Topological groups, Lie groups. From Lie groups, we get Lie algebras via a standard procedure in differential topology. There’s also an association in the reverse direction, from Lie algebras to Li...

We use a fermionic extension of the bosonic module to obtain a class of B(0, N)-graded Lie superalgebras with nontrivial central extensions. 0 Introduction B(M − 1, N)-graded Lie superalgebras were first investigated and classified up to central extension by Benkart-Elduque (see also Garcia-Neher’s work in [GN]). Those root graded Lie superalgebras are a super-analog of root graded Lie algebras...

The theory of Lie algebras has many applications in mathematics and physics. One possible way of generalizing the theory of Lie algebras is to develop the theory of Lie-like algebras algebras, where the notion of a Lie-like algebras algebra was introduced in [4]. One of Lie’s Theorems claims that the only irreducible representations of a solvable Lie algebra over an algebraically closed field k...

Introduction 1 1. Preliminaries 6 2. Generic stabilisers (centralisers) for the adjoint representation 9 3. Generic stabilisers for the coadjoint representation 10 4. Semi-direct products of Lie algebras and modules of covariants 12 5. Generic stabilisers and rational invariants for semi-direct products 14 6. Reductive semi-direct products and their polynomial invariants 21 7. Takiff Lie algebr...

The construction of a class of associative composition algebras qn on R 4 generalizing the wellknown quaternions Q provides an explicit representation of the universal enveloping algebra of the real three-dimensional Lie algebras having tracefree adjoint representations (class A Bianchi type Lie algebras). The identity components of the four-dimensional Lie groups GL(qn,l) Cqn (general linear g...

In this paper, we classify the indecomposable non-nilpotent solvable Lie algebras with $N(R_n,m,r)$ nilradical,by using the derivation algebra and the automorphism group of $N(R_n,m,r)$.We also prove that these solvable Lie algebras are complete and unique, up to isomorphism.