Another definition is that higher-spin algebras are quotients of the universal enveloping algebra of the anti-de Sitter algebra so ( d, 2 ) by certain two-sided ideals.
32.
The universal enveloping algebra of the Heisenberg algebra is the Weyl algebra ( modulo the relation that the center be the unit ); here, the \ star product is called the Moyal product.
33.
Springer correspondence turned out to be closely related to the classification of primitive ideals in the universal enveloping algebra of a complex semisimple Lie algebra, both as a general principle and as a technical tool.
34.
Sometimes, the Lie superalgebra is embedded within A in the sense that there is a homomorphism from the universal enveloping algebra of the Lie superalgebra to A . In that case, the equation above reduces to
35.
In the case of the " K "-invariant elements of the universal enveloping algebra for a maximal compact subgroup " K ", the Harish-Chandra homomorphism was studied by.
36.
Since \ mathfrak { g } is a module over itself via adjoint representation, the enveloping algebra U ( \ mathfrak { g } ) becomes a \ mathfrak { g }-module by extending the adjoint representation.
37.
One starts by defining the quasi-triangular Hopf algebras, and then performing what is called a quantum deformation to obtain the "'quantum universal enveloping algebra "', or quantum group, for short.
38.
Equivalently, a representation of " L " is a "'Z "'2-graded representation of the universal enveloping algebra of " L " which respects the third equation above.
39.
Duflo has worked on the orbit method of Alexander Kirillov . He introduced the Duflo isomorphism, an isomorphism between the center of the enveloping algebra of a finite-dimensional Lie algebra and the invariants of its symmetric algebra.
40.
The formal group ring of a formal group law is a cocommutative Hopf algebra analogous to the group ring of a group and to the universal enveloping algebra of a Lie algebra, both of which are also cocommutative Hopf algebras.
