Lie algebra


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Lie algebra

[′lē ‚al·jə·brə]
(mathematics)
The algebra of vector fields on a manifold with additive operation given by pointwise sum and multiplication by the Lie bracket.
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i) [GAMMA](E) is endowed with a Lie algebra structure [,] over R,
Let U be the complexified universal enveloping algebra of the real Lie algebra g of G; which is canonically isomorphic onto the algebra of all distributions on G supported by {0} , where 0 is the identity element of G.
The structure of Hopf co-Poisson algebra on the universal enveloping algebra U(ST(2)) of Lie algebra ST(2) is determined with the help of a solution of the Yang-Baxter equation.
angle](G) is the Lie algebra of the group G, rad G is the radical of G, and [G.
For example for the semisimple complex finite-dimensional Lie algebra g we have [U.
In [LP], Lam and Pylyavskyy introduced the electrical Lie algebra [el.
It is not about mathematics, he says, but about the use of symmetries, mainly described by the techniques of Lie groups and Lie algebra.
C) Compact case: g is the Lie algebra of a compact simple Lie group.
lambda]](q) is the graded character of a simple Lie algebra coming from tensor products of KR modules.
n] satisfying Poisson brackets or as a quantum system with the generators of the Lie algebra sl (2) and commutation relations
Lie-Rinehart algebras, also known as Lie algebroids, give rise to Hopf algebroids by a universal enveloping algebra construction, much as the universal enveloping algebra of an ordinary Lie algebra gives a Hopf algebra, of infinite dimension.
By the classical Lie theory, the Lie algebra of a compact Lie group is a direct product of an abelian Lie algebra and some simple Lie algebras.