Group-like Structures in Quantum Lie Algebras and the Process of Quantization

Details Group-like Structures in Quantum Lie Algebras and the Process of Quantization Group-like Structures in Quantum Lie Algebras and the Process of Quantization

1994-05-06

arxiv.org/abs/hep-th/9405045v1

Physics

High Energy Physics

High Energy Physics - Theory

10 pages

Scientific paper

For a certain class of Lie bialgebras $(A,A^*)$ the corresponding quantum universal enveloping algebras $U_q(A)$ are prooved to be equivalent to quantum groups Fun$_q(F^*)$, $F^*$ being the factor group for the dual group $G^*$. This property can be used to simplify the process of quantization. The described class appears to be wide enough to contain all the standard quantizations of infinite series. The properties of the groups $F^*$ are explicitly demonstrated for the standard deformations $U_q(SL(n))$. It is shown that for different $A^*$ (remaining in the described class of Lie bialgebras) the same algorithm leads to the nonstandard quantizations.

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