## Abstract

Motivated by the study of symmetries of (Formula presented.) -algebras, as well as by multivariate operator theory, we introduce the notion of an (Formula presented.) -equivariant subproduct system of Hilbert spaces. We analyse the resulting Toeplitz and Cuntz–Pimsner algebras and provide results about their topological invariants through Kasparov's bivariant (Formula presented.) -theory. In particular, starting from an irreducible representation of (Formula presented.), we show that the corresponding Toeplitz algebra is equivariantly (Formula presented.) -equivalent to the algebra of complex numbers. In this way, we obtain a six-term exact sequence of (Formula presented.) -groups containing a noncommutative analogue of the Euler class.

Original language | English |
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Journal | Transactions of the London Mathematical Society |

Volume | 8 |

Issue number | 1 |

Pages (from-to) | 440-492 |

ISSN | 2052-4986 |

DOIs | |

Publication status | Published - Dec 2021 |