Results 231 to 240 of about 1,969,963 (254)

THE WEYL GROUP OF A GRADED LIE ALGEBRA

, 1976
The action of the group G0 of fixed points of a semisimple automorphism θ of a reductive algebraic group G on an eigenspace V of this automorphism in the Lie algebra g of the group G is considered.
E. Vinberg
semanticscholar   +1 more source

Classification of all simple graded Lie algebras whose Lie algebra is reductive. I

, 1976
All simple graded Lie algebras whose Lie algebra is reductive are presented, and the classification theorem is proved. Several theorems which may show up to be useful in a different context are also included.
M. Scheunert, W. Nahm, V. Rittenberg
semanticscholar   +1 more source

On algebraically irreducible representations of the Lie algebra sl(2)

, 1974
An algebraic study of the irreducible representations of the complex Lie algebra sl(2) is presented in this article. This study generalizes a former series of works of W. Miller. Though the list is not complete, it gives hints as to the construction of a
D. Arnal, G. Pinczon
semanticscholar   +1 more source

Structure of the standard modules for the affine Lie algebra A[(1)] [1]

, 1985
The Lie algebra $A_1^(1)$ The category $\cal P_k$ The generalized commutation relations Relations for standard modules Basis of $\Omega_L$ for a standard module $L$ Schur functions Proof of linear independence Combinatorial formulas.
J. Lepowsky, M. Primc
semanticscholar   +1 more source

COHOMOLOGY OF THE LIE ALGEBRA OF FORMAL VECTOR FIELDS

, 1970
We calculate the cohomology of the Lie algebra of formal vector fields at the origin in a euclidean space. The results are applied to the investigation of the Lie algebra of tangent vector fields on a smooth manifold.
I. Gel'fand, D. B. Fuks
semanticscholar   +1 more source

Nilpotent Lie Algebras and Solvable Lie Algebras

1987
The Lie algebras considered in this chapter are finite-dimensional algebras over a field k. In Sees. 7 and 8 we assume that k has characteristic 0. The Lie bracket of x and y is denoted by [x, y], and the map y → [x, y] by ad x.
openaire   +2 more sources

Lie Groups and Lie Algebras [PDF]

, 1976
As we pointed out in 6.2, there are exactly two simple real Lie algebras of dimension 3. These are: the algebra \( {{\mathfrak{g}}_{1}} = \mathfrak{s}\mathfrak{l}\left( {2,R} \right) \) of real matrices of the second order with zero trace and the algebra \( {{\mathfrak{g}}_{2}} = \mathfrak{s}\mathfrak{o} = \left( {3,R} \right) \) of real skew-symmetric
openaire   +1 more source

Lie Algebras, Lie Groups, and Algebra of Incidence

2018
We have learned that readers of the work of D. Hestenes and G. Sobzyk (Hestenes and Sobczyk (1984). Clifford Algebra to Geometric Calculus: A Unified Language for Mathematics and Physics.) [138] Chap. 8 and a late article of Ch. Doran, D. Hestenes and F. Sommen (Doran, Hestenes, Sommen and Van Acker (1993).
openaire   +2 more sources

Lie Groups and Lie Algebras

1988
Whereas discrete groups mainly describe the symmetries of regular geometric structures (crystals), continuous groups are essential in discussing the properties of particles, fields (atoms and all the more elementary particles) and conservation laws. We restrict the investigation here to Lie groups and the Lie algebras connected with them.
W. Ludwig, Claus Falter
openaire   +2 more sources

Biderivations and linear commuting maps on the Lie algebra

, 2017
Xiao Cheng, Minjing Wang, Jiancai Sun, Honglian Zhang   +3 more
semanticscholar   +1 more source