Property (T) for C * ‐Algebras | Zendy

Bekka Bachir | Zendy

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Property (T) for C * ‐Algebras

Author(s) -

Bekka Bachir

Publication year - 2006

Publication title -

bulletin of the london mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.396

H-Index - 48

eISSN - 1469-2120

pISSN - 0024-6093

DOI - 10.1112/s0024609306018765

Subject(s) - mathematics , subalgebra , property (philosophy) , unital , discrete group , group (periodic table) , mathematics subject classification , state (computer science) , combinatorics , pure mathematics , discrete mathematics , algebra over a field , philosophy , epistemology , algorithm , chemistry , organic chemistry

A notion of Property (T) is defined for an arbitrary unital C*‐algebra A admitting a tracial state. This is extended to a notion of Property (T) for a pair ( A, B ) where B is a C*‐subalgebra of A . Let Γ be a discrete group andC r * ( Γ )its reduced algebra. We show thatC r * ( Γ )has Property (T) if and only if the group Γ has Property (T). More generally, given a subgroup Λ of Γ, the pair( C r * ( Γ ) , C r * ( Λ ) )has Property (T) if and only if the pair of groups (Γ, Λ) has Property (T). 2000 Mathematics Subject Classification 46L05, 22D25.

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