English

Infinite-dimensional Compact Quantum Semigroup

Quantum Algebra 2012-12-04 v1 Functional Analysis Operator Algebras

Abstract

In this paper we construct a compact quantum semigroup structure on the Toeplitz algebra T\mathcal{T}. The existence of a subalgebra, isomorphic to the algebra of regular Borel's measures on a circle with convolution product, in the dual algebra T\mathcal{T}^* is shown. The existence of Haar functionals in the dual algebra and in the above-mentioned subalgebra is proved. Also we show the connection between T\mathcal{T} and the structure of weak Hopf algebra.

Keywords

Cite

@article{arxiv.1104.4820,
  title  = {Infinite-dimensional Compact Quantum Semigroup},
  author = {Marat A. Aukhadiev and Suren A. Grigoryan and Ekaterina V. Lipacheva},
  journal= {arXiv preprint arXiv:1104.4820},
  year   = {2012}
}

Comments

17 pages

R2 v1 2026-06-21T17:58:36.856Z