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Abstrak :
Aljabar Lie adalah ruang vektor atas suatu lapangan yang dilengkapi dengan bracket Lie yang bilinier, bersifat antisimetri dan memenuhi identitas Jacobi. Salah satu contoh dari aljabar Lie adalah himpunan pemetaan linier dari ruang vektor V ke V, yang dinotasikan dengan gl(V), dengan bracket Lie berupa komutator. Jika V adalah suatu aljabar, maka himpunan derivasi dari V (dinotasikan dengan Der(V)) membentuk suatu subaljabar Lie dari gl(V). Holomorph dari aljabar Lie L, yaitu hasil tambah langsung dari L dan Der(L), juga membentuk aljabar Lie. Aljabar Lie dikatakan lengkap jika pusatnya adalah himpunan nol dan semua derivasinya adalah derivasi dalam. Pada tesis ini, diulas syarat yang harus dipenuhi agar aljabar derivasi dan holomorph dari suatu aljabar Lie menjadi lengkap. ......Lie algebra is a vector space over a field together with a bilinear Lie bracket, that satisfy antisymmetry and Jacobi identity. One of the examples of Lie algebra is a set of linear transformation from a vector space V to V, that is denoted by gl(V), with a commutator as the Lie bracket. If V is an algebra then the set of derivation of V (denoted by Der(V)) forms a Lie subalgebra of gl(V). The holomorph of a Lie algebra, that is direct sum of vector spaces L and Der(L), also forms a Lie algebra. A Lie algebra is called complete if its center is zero and all its derivations are inner. In this thesis, it is discussed the properties that must be satisfied in order to the derivation and the holomorph of Lie algebra become complete.

Abstrak :
Aljabar Lie sederhana merupakan aljabar Lie dengan karakteristik khusus, yaitu tidak abelian dan tidak memiliki ideal sejati yang tak nol. Dalam penelitian ini, dikenalkan suatu aljabar Lie sederhana yaitu sl fr infin;,K yang merupakan subaljabar Lie dari gl fr infin;,K . Aljabar Lie sederhana sl fr infin;,K memiliki dimensi yang tidak berhingga dengan basis yang tak terhitung. ...... Simple Lie algebra is Lie algebra with special characteristics, which is not abelian and not having any nonzero proper ideal. In this study, a simple Lie algebra sl fr infin ,K is introduced, which is a sub Lie algebra from gl fr infin ,K . Simple Lie algebra sl fr infin ,K has an infinitely dimension with an uncountably basis.

Abstrak :
Introduces the concepts and methods of the Lie theory in a form accessible to the non-specialist by keeping mathematical prerequisites to a minimum. Although the authors have concentrated on presenting results while omitting most of the proofs, they have compensated for these omissions by including many references to the original literature. Their treatment is directed toward the reader seeking a broad view of the subject rather than elaborate information about technical details. Illustrations of various points of the Lie theory itself are found throughout the book in material on applications. In this reprint edition, the authors have resisted the temptation of including additional topics. Except for correcting a few minor misprints, the character of the book, especially its focus on classical representation theory and its computational aspects, has not been changed.

Abstrak :
Presents the real inner product spaces of arbitrary (finite or infinite) dimension greater than or equal to 2. This book studies the sphere geometries of Mobius and Lie for these spaces, besides euclidean and hyperbolic geometry, as well as geometries where Lorentz transformations play the key role.

Abstrak :
This monograph provides the first up-to-date and self-contained presentation of a recently discovered mathematical structure—the Schrödinger-Virasoro algebra. Just as Poincaré invariance or conformal (Virasoro) invariance play a key rôle in understanding, respectively, elementary particles and two-dimensional equilibrium statistical physics, this algebra of non-relativistic conformal symmetries may be expected to apply itself naturally to the study of some models of non-equilibrium statistical physics, or more specifically in the context of recent developments related to the non-relativistic AdS/CFT correspondence. The study of the structure of this infinite-dimensional Lie algebra touches upon topics as various as statistical physics, vertex algebras, Poisson geometry, integrable systems and supergeometry as well as representation theory, the cohomology of infinite-dimensional Lie algebras, and the spectral theory of Schrödinger operators.