A group algebra for inductive limit groups. Continuity problems of the canonical commutation relations

DOI10.1023/A:1017988601883zbMath0871.22002MaRDI QIDQ1355862

Hendrik B. G. S. Grundling

Publication date: 24 September 1997

Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)

zbMATH Keywords

\(C^*\)-algebrarepresentationsmultiplier algebraquantum systemssymplectic group actionsCCR-algebrainductive limit grouptwisted discrete group algebra

Mathematics Subject Classification ID

Representations of general topological groups and semigroups (22A25) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Axiomatic quantum field theory; operator algebras (81T05) Applications of selfadjoint operator algebras to physics (46L60) Group algebras of locally compact groups (22D15) Measure algebras on groups, semigroups, etc. (43A10)

Related Items (9)

Some continuous field quantizations, equivalent to the \(C^*\)-Weyl quantization ⋮ FULL REGULARITY FOR A C*-ALGEBRA OF THE CANONICAL COMMUTATION RELATIONS ⋮ Construction and uniqueness of the C*-Weyl algebra over a general pre-symplectic space ⋮ Operator-algebraic construction of gauge theories and Jones' actions of Thompson's groups ⋮ Classical limits of gauge-invariant states and the choice of algebra for strict quantization ⋮ Quantization as a categorical equivalence ⋮ The resolvent algebra: A new approach to canonical quantum systems ⋮ Representations of \(^\ast\)-algebras by unbounded operators: C\(^\ast\)-hulls, local-global principle, and induction ⋮ The resolvent algebra: ideals and dimension

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