Faithful representations of crossed products by actions of $\boldsymbol N^k$ | Zendy

Nadia S. Larsen | Zendy; Iain Raeburn | Zendy

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Faithful representations of crossed products by actions of $\boldsymbol N^k$

Author(s) -

Nadia S. Larsen,

Iain Raeburn

Publication year - 2001

Publication title -

mathematica scandinavica

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.553

H-Index - 30

eISSN - 1903-1807

pISSN - 0025-5521

DOI - 10.7146/math.scand.a-14342

Subject(s) - endomorphism , mathematics , hecke algebra , semigroup , pure mathematics , algebra over a field , structured program theorem

We study a family of semigroup crossed products arising from actions of $\boldsymbol N^k$ by endomorphisms of groups. These include the Hecke algebra arising in the Bost-Connes analysis of phase transitions in number theory, and other Hecke algebras considered by Brenken. Our main theorem is a characterisation of the faithful representations of these crossed products, and generalises a similar theorem for the Bost-Connes algebra due to Laca and Raeburn.

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