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

1994/05/06 by V. D. Lyakhovsky, Lyakhovsky, V. D.
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.hep-th/9405045

openalex publication_date 1994/05/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Related

• Quantization of Lie bialgebras, I
• The Role of Solvable Groups in Quantization of Lie Algebras
• Quantum algebras and Lie groups
• Quantum differential operators on the quantum plane
• Quantization of Lie bialgebras, II