Nica-Toeplitz algebras associated with product systems over right LCM semigroups

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:470

Article

Kwasniewski, Bartosz K.¹  Larsen, Nadia S.² 

[1] Univ Bialystok, Inst Math, Ul K Ciolkowskiego 1M, PL-15245 Bialystok, Poland

[2] Univ Oslo, Dept Math, POB 1053 Blindern, N-0316 Oslo, Norway

关键词: Right LCM scmigroup;    C*-correspondence;    Nica-Toeplitz crossed product;    Semigroup C*-algebra;   

DOI  :  10.1016/j.jmaa.2018.10.020

来源: Elsevier

【 摘 要 】

We prove uniqueness of representations of Nica-Toeplitz algebras associated to product systems of C*-correspondences over right LCM semigroups by applying our previous abstract uniqueness results developed for C*-precategories. Our results provide an interpretation of conditions identified in work of Fowler and Fowler-Raeburn, and apply also to their crossed product twisted by a product system, in the new context of right LCM semigroups, as well as to a new, Doplicher-Roberts type C*-algebra associated to the Nica-Toeplitz algebra. As a derived construction we develop Nica-Toeplitz crossed products by actions with completely positive maps. This provides a unified framework for Nica-Toeplitz semigroup crossed products by endomorphisms and by transfer operators. We illustrate these two classes of examples with semigroup C*-algebras of right and left semidirect products. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free