Acknowledgement
This work was supported by the Natural Science Foundation of Shandong Province (Nos. ZR2020MA008 and ZR2019MA039), the China Postdoctoral Science Foundation (No. 2018M642633), and the National Natural Science Foundation of China (No. 11871303).
References
- B. Blackadar, Operator algebras, Encyclopaedia of Mathematical Sciences, 122, Springer-Verlag, Berlin, 2006. https://doi.org/10.1007/3-540-28517-2
- N. P. Brown and N. Ozawa, C*-algebras and finite-dimensional approximations, Graduate Studies in Mathematics, 88, American Mathematical Society, Providence, RI, 2008. https://doi.org/10.1090/gsm/088
- J. Crisp and M. Laca, On the Toeplitz algebras of right-angled and finite-type Artin groups, J. Aust. Math. Soc. 72 (2002), no. 2, 223-245. https://doi.org/10.1017/S1446788700003876
- B. Deroin, A. Navas and C. Rivas, Groups, orders, and dynamics, arXiv:1408.5805v2.
- S. Y. Jang, Reduced crossed products by semigroups of automorphisms, J. Korean Math. Soc. 36 (1999), no. 1, 97-107.
- M. Laca, From endomorphisms to automorphisms and back: dilations and full corners, J. London Math. Soc. (2) 61 (2000), no. 3, 893-904. https://doi.org/10.1112/S0024610799008492
- M. Laca and I. Raeburn, Semigroup crossed products and the Toeplitz algebras of non-abelian groups, J. Funct. Anal. 139 (1996), no. 2, 415-440. https://doi.org/10.1006/jfan.1996.0091
- C. Lance, On nuclear C*-algebras, J. Funct. Anal. 12 (1973), 157-176. https://doi.org/10.1016/0022-1236(73)90021-9
- X. Li, Semigroup C*-algebras and amenability of semigroups, J. Funct. Anal. 262 (2012), no. 10, 4302-4340. https://doi.org/10.1016/j.jfa.2012.02.020
- X. Li, Nuclearity of semigroup C*-algebras and the connection to amenability, Adv. Math. 244 (2013), 626-662. https://doi.org/10.1016/j.aim.2013.05.016
- A. McKee, A. Skalski, I. G. Todorov, and L. Turowska, Positive Herz-Schur multipliers and approximation properties of crossed products, Math. Proc. Cambridge Philos. Soc. 165 (2018), no. 3, 511-532. https://doi.org/10.1017/S0305004117000639
- G. J. Murphy, Ordered groups and crossed products of C*-algebras, Pacific J. Math. 148 (1991), no. 2, 319-349. http://projecteuclid.org/euclid.pjm/1102644690 102644690
- G. J. Murphy, C*-algebras generated by commuting isometries, Rocky Mountain J. Math. 26 (1996), no. 1, 237-267. https://doi.org/10.1216/rmjm/1181072114
- A. Nica, C*-algebras generated by isometries and Wiener-Hopf operators, J. Operator Theory 27 (1992), no. 1, 17-52.
- A. L. T. Paterson, Amenability, Mathematical Surveys and Monographs, 29, American Mathematical Society, Providence, RI, 1988. https://doi.org/10.1090/surv/029
- M. Rordam, Classification of nuclear, simple C*-algebras, in Classification of nuclear C*-algebras.C*-algebras. Entropy in operator algebras, 1-145, Encyclopaedia Math. Sci., 126, Oper. Alg. Non-commut. Geom., 7, Springer, Berlin, 2002. https://doi.org/10.1007/978-3-662-04825-2_1