مطالعه مرز فرستنبرگ برای زوج گروه ها

نویسندگان
محمد باقر اسدی
زهرا حسن پور یخدانی
دانشگاه تهران
چکیده
ﺩﺭ ﺍیﻦ ﻣﻘﺎﻟﻪ، ﺑﺎ ﻓﺮﺽ ﺁﻥ که G ﮔﺮﻭﻩ ﺗﻮﭘﻮﻟﻮﮊیک ﮔﺴﺴﺘﻪ ﻭ H یک ﺯیﺮﮔﺮﻭﻩ ﺁﻥ ﺍﺳﺖ، ﺑﻪ ﺑﯿﺎﻥ ﻣﻔﻬﻮﻡ ) H(G, ﺳﯿﺴﺘﻢ ﻋﻤلگرﯼ ﭘﺮﺩﺍﺧﺘﻪ ﻭ ﻣﺮﺯ ﻫﺎﻣﺎﻧﺎ ﺑﺮﺍﯼ ﺯﻭﺝ ﮔﺮﻭەﻫﺎﯼ ) H(G, ﺭﺍ ﺗﻌﺮیﻒ ﻧﻤﻮﺩەﺍیﻢ. ﺩﺭﻭﺍﻗﻊ، ﻧﺸﺎﻥ ﺩﺍﺩەﺍیﻢ ﮐﻪ ﻣﺮﺯ ﻓﺮﺳﺘﻨﺒﺮﮒ ﺑﺮﺍﯼ ﺯﻭﺝ ﮔﺮﻭەﻫﺎ ﺑﺎ ﻣﺮﺯ ﻫﺎﻣﺎﻧﺎ ﺑﺮﺍﯼ ﺯﻭﺝ ﮔﺮﻭەﻫﺎ، ﻫﻤﺮیﺨﺖ ﺍﺳﺖ. ﺑﻪ ﺑﯿﺎﻥ ﺩیگر، ﺗﻌﻤﯿﻢ طبیعی نظریه ﮐﻼﺳﯿک ﻣﺮﺯﻫﺎﯼ ﻓﺮﺳﺘﻨﺒﺮﮒ ﺑﺮﺍﯼ ﻣﺮﺯ ﻓﺮﺳﺘﻨﺒﺮﮒ ﺑﺮﺍﯼ ﺯﻭﺝ ﮔﺮﻭەﻫﺎﯼ ) H(G, ﻧﯿﺰ ﺑﺮﻗﺮﺍﺭ ﺍﺳﺖ.
کلیدواژه‌ها
ﻣﺮﺯ ﻓﺮﺳﺘﻨﺒﺮﮒ
ﻣﺮﺯ ﻫﺎﻣﺎﻧﺎ
ﭘﻮﺷﺶ ﺍﻧﮋﮐﺘﯿﻮ

عنوان مقاله English

A Study of the Furstenberg Boundary for Pair of Groups

نویسندگان English

Mohammad Bagher Asadi
Zahra Hassanpour-Yakhdani
University of Tehran
چکیده English

In this paper, assuming that G is a discrete topological group and H is a subgroup of G, we introduce the notion of a (G, H)-operator system and define the Hamana boundary for pairs of groups (G, H). In fact, we show that the Furstenberg boundary for pairs of groups is isomorphic to the Hamana boundary for pairs of groups. In other words, the natural extension of the classical theory of Furstenberg boundaries remains valid for the Furstenberg boundary associated with pairs of groups (G, H).

کلیدواژه‌ها English

Furstenberg boundary
Hamana boundary
Injective envelope
[۱] H. Furstenberg, Boundary theory and stochastic processes on homogeneous spaces, Proc. Symp.

Pure Math. 26 (1973).

[۲] M. Hamana, Injective envelopes of operator systems, Publ. RIMS 15 (1979), 773–785. [۳] M. Hamana, Injective envelopes of C∗-algebras, J. Math. Soc. Japan, 37 (1985), 139-158. [۴] N. Monod, Furstenberg boundaries for pairs of groups, arXiv:1301.7749.

[۵] B. Kalantar, M. Kennedy, Boundaries of reduced C*-algebras of discrete groups, J. Reine Angew.

Math. 727 (2016), 247–267.