发表机构
National and Kapodistrian University of Athens（雅典国立卡波迪斯特里阿斯大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究积系统生成的C*-代数的精确性与核性，证明其等价于核或系数代数的相应性质，并指出紧对齐假设的必要性。
AI 中文摘要
我们研究由可数离散群的幺元子半群上的积系统的表示生成的C*-代数。在第一部分中，我们证明所生成的C*-代数的精确性等价于其在可构造理想上的核的精确性。所生成的C*-代数的核性等价于核在不动点代数中的核嵌入性。在第二部分中，我们进一步研究单射等变Fock协变表示，以及核的性质是否从系数C*-代数的性质继承而来，如同右LCM半群上紧对齐饱和积系统的情况。若半群是有限对齐的且积系统是饱和且紧对齐的，则核的精确性等价于系数C*-代数的精确性。若此外半群是强有限对齐的，则核的核嵌入性等价于系数C*-代数的核嵌入性。这些结果在无紧对齐假设时不成立，即使对右LCM半群也是如此。
英文摘要
We study C*-algebras generated by representations of product systems over unital subsemigroups of amenable discrete groups. In the first part, we show that exactness of the generated C*-algebra is equivalent to exactness of the cores over the constructible ideals. Nuclearity of the generated C*-algebra is equivalent to nuclear embeddability of the cores in the fixed point algebra. In the second part, we further study injective equivariant Fock covariant representations, and whether the properties of the cores are inherited from properties of the coefficient C*-algebra, as in the case of compactly aligned saturated product systems over right LCM semigroups. If the semigroup is finitely aligned and the product system is saturated and compactly aligned, then exactness of the cores is equivalent to exactness of the coefficient C*-algebra. If in addition the semigroup is strongly finitely aligned, then nuclear embeddability of the cores is equivalent to nuclear embeddability of the coefficient C*-algebra. These results do not hold without the compact alignment hypothesis, even for right LCM semigroups.
Comments38 pages
