Advances in Operator Theory

Quantum groups, from a functional analysis perspective

Teodor Banica

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Abstract

‎It is well-known that any compact Lie group appears as closed subgroup of a unitary group‎, ‎$G\subset U_N$‎. ‎The unitary group $U_N$ has a free analogue $U_N^+$‎, ‎and the study of the closed quantum subgroups $G\subset U_N^+$ is a problem of general interest‎. ‎We review here the basic tools for dealing with such quantum groups‎, ‎with all the needed preliminaries included‎, ‎and we discuss as well a number of more advanced topics‎.

Article information

Source
Adv. Oper. Theory, Volume 4, Number 1 (2019), 164-196.

Dates
Received: 11 April 2018
Accepted: 8 May 2018
First available in Project Euclid: 8 June 2018

Permanent link to this document
https://projecteuclid.org/euclid.aot/1528444819

Digital Object Identifier
doi:10.15352/aot.1804-1342

Mathematical Reviews number (MathSciNet)
MR3867340

Zentralblatt MATH identifier
06946449

Subjects
Primary: 46L65: Quantizations, deformations
Secondary: 46L89: Other "noncommutative" mathematics based on C-algebra theory [See also 58B32, 58B34, 58J22]

Keywords
quantum group ‎free unitary group ‎operator algebra

Citation

Banica, Teodor. Quantum groups, from a functional analysis perspective. Adv. Oper. Theory 4 (2019), no. 1, 164--196. doi:10.15352/aot.1804-1342. https://projecteuclid.org/euclid.aot/1528444819


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