mathematics, a quantum or quantized enveloping algebra is a q-analog of a universal enveloping algebra. Given a Lie algebra g {\displaystyle {\mathfrak...

called a deformation quantization of a {\displaystyle {\mathfrak {a}}} . A quantized enveloping algebra. The dual of such an algebra turns out to be an...

equivalent but larger, namely a group algebra or a universal enveloping algebra, then a group algebra or enveloping algebra can be "deformed", although the...

Albert algebra, an exceptional Jordan algebra that is not enveloped by the canonical construction of the enveloping algebra for Jordan algebras. List of...

the tensor algebra of any Lie algebra is a Poisson algebra. The universal enveloping algebra is obtained by modding out the Poisson algebra structure....

category. Lusztig, George (1991), "Quivers, perverse sheaves, and quantized enveloping algebras", Journal of the American Mathematical Society, 4 (2): 365–421...

representations of a quantized enveloping algebra of type A D E {\displaystyle ADE} and also for the plus part of that algebra was introduced by Lusztig...

the unit of the universal enveloping algebra (called 1 above). The algebra W(V) is a quantization of the symmetric algebra Sym(V). If V is over a field...

States and works at the University of Chicago. Drinfeld's work connected algebraic geometry over finite fields with number theory, especially the theory...

pp. 147–159 George Lusztig, Quivers, perverse sheaves, and quantized enveloping algebras, Journal of the American Mathematical Society 4 (1991), no....

{sl}}_{2}\hookrightarrow {\mathfrak {g}}} , a W-algebra may be constructed from the universal enveloping algebra of the affine Lie algebra g ^ {\displaystyle {\hat {\mathfrak...

a universal enveloping algebra follows from the fact that the Weyl algebra is the universal enveloping algebra of the Heisenberg algebra (modulo that...

quantum quantum group. quantized quantized enveloping algebra. radical 1.  The radical of a Lie group. 2.  The radical of a Lie algebra g {\displaystyle {\mathfrak...

algebra as describing a certain "non-standard" or "quantized" algebraic group (which is not an algebraic group at all). While there does not seem to be a...

the universal enveloping algebra U ( h n ) {\displaystyle U({\mathfrak {h}}_{n})} . Among other properties, the universal enveloping algebra is an associative...

affine algebra (or affine quantum group) is a Hopf algebra that is a q-deformation of the universal enveloping algebra of an affine Lie algebra. They were...

about is given in the universal enveloping algebra article. Quantum deformations of the universal enveloping algebra lead to the notion of quantum groups...

Dixmier's enveloping algebras may be thought of as working out non-commutative algebraic geometry for the primitive spectrum of an enveloping algebra of a...

(1992). "Local Finiteness of the Adjoint Action for Quantized Enveloping Algebras". Journal of Algebra. 153 (2): 289–318. doi:10.1016/0021-8693(92)90157-H...

S2CID 121695684 Lusztig, G. (1990), "Canonical bases arising from quantized enveloping algebras", Journal of the American Mathematical Society, 3 (2): 447–498...

construction is an embedding of the Virasoro algebra into the universal enveloping algebra of the affine Lie algebra. The existence of the embedding shows that...

the Lie algebra generated by X and Y. The universal enveloping algebra of the free Lie algebra generated by X and Y is isomorphic to the algebra of all...

different eigenspaces of the Casimir invariants of the universal enveloping algebra for those symmetries. This is the case for both the Lorentz symmetry...

(v\otimes w)=w\otimes v} . The category of representations of a quantized universal enveloping algebra U q ( g ) {\displaystyle U_{q}({\mathfrak {g}})} is a braided...

works were influenced by the quantum group theory. He discovered that quantized algebra of functions Funq(GL) can be defined by the requirement that T and...

C^{*}} -algebra A {\displaystyle A} , the closure of Φ ( A ) {\displaystyle \Phi (A)} in the weak operator topology is called the enveloping von Neumann...

introduced the quantized Schur algebras (or q-Schur algebras for short), which are a type of q-deformation of the classical Schur algebras described above...

respect to the largest possibly C*-norm gives its enveloping C*-algebra, called the group C*-algebra C*(G) of G. (Any C*-norm on L1(G) is bounded by the...

1993. Kostant's work has involved representation theory, Lie groups, Lie algebras, homogeneous spaces, differential geometry and mathematical physics, particularly...

formulation. The universal enveloping algebra U ( g l n ) {\displaystyle U({\mathfrak {gl}}_{n})} can be defined as an algebra generated by Eij subject...