Results 271 to 280 of about 2,694 (314)

Lie algebras of nonstandard relativity groups

Czechoslovak Journal of Physics, 2002
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Barashenkov, V. S., Kapuścik, E., Wcislo, D.   +2 more
openaire   +1 more source

Representability of Lie Algebras and Lie Groups by Matrices

The Annals of Mathematics, 1937
1. Jede Liesche Algebra (Infinitesimalgruppe) \(L\) kann in einen assoziativen Ring (und zwar in eine Algebra mit unendlicher Basis) so eingebettet werden, daß \([xy] = xy - yx\) wird. 2. Alle möglichen kleinsten Ringe, in denen eine solche Einbettung möglich ist, können aus einem einzigen solchen Ring, der eindeutig durch \(L\) bestimmt ist, durch ...
openaire   +2 more sources

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   +1 more source

Lie Algebras of Pro-Affine Algebraic Groups

Canadian Journal of Mathematics, 2002
AbstractWe extend the basic theory of Lie algebras of affine algebraic groups to the case of pro-affine algebraic groups over an algebraically closed fieldKof characteristic 0. However, some modifications are needed in some extensions. So we introduce the pro-discrete topology on the Lie algebra ℒ(G) of the pro-affine algebraic groupGoverK, which is ...
openaire   +1 more source

The Lie Algebra of a Lie Group

2017
The Lie algebra of a Lie group is introduced via the tangent space and distributions and differential operators are discussed and used in this setting.
openaire   +1 more source

RESTRICTED LIE ALGEBRAS OF POLYCYCLIC GROUPS

Journal of Algebra and Its Applications, 2006
We consider some classes of polycyclic groups which have a p-series such that the restricted graded Lie algebra associated to this p-series is free abelian. We also study p-series and restricted Lie algebras associated to them in arbitrary polycyclic groups.
openaire   +1 more source

Automorphism Groups of Nilpotent Lie Algebras

Journal of the London Mathematical Society, 1987
It is shown that every linear algebraic group (over an arbitrary field) arises from some nilpotent Lie algebra \(L\) as the group of linear transformations induced on the commutator quotient \(L/[L,L]\) by the automorphism group of \(L\). More precisely, let \(k\) be a field and let \(K\) be an extension field of \(k\).
openaire   +2 more sources

Representation of Lie Groups and Lie Algebras

2013
The representation of Lie groups is closely related to the representation of their Lie algebras, and we shall discuss them later in this chapter. In the case of compact groups, however, there is a well developed representation theory, which we shall consider in the first section.
openaire   +1 more source

Some examples of Lie groups and Lie algebras

Siberian Mathematical Journal, 1972
We p r e s e n t s o m e e x a m p l e s of l o c a l l y s o l v a b l e s e m i s i m p l e L i e a l g e b r a s tha t a r e not RN* a l g e b r a s , a s w e l l a s e x a m p l e s of l o c a l l y n i lpo ten t RN* L i e a l g e b r a s wi th n e i t h e r Engel e l e m e n t s , nor (of cou r se ) a c c e s s i b l e e l e m e n t s (for de f i ...
openaire   +2 more sources

Prederivations of Lie Algebras and Isometries of Bi-invariant Lie Group

Geometriae Dedicata, 1997
The author studies some of the properties of (skew-symmetric) prederivations of Lie algebras and derives some results on the isometry groups of bi-invariant Lie groups. Conditions under which a complex Lie group with a bi-invariant Norden metric has only holomorphic isometries are given.
openaire   +1 more source