Property T for locally compact quantum groups.

In this short paper, we obtained some equivalent formulations of property T for a general locally compact quantum group 픾, in terms of the full quantum group C*-algebras and the *-representation of associated with the trivial unitary corepresentation (that generalize the corresponding results for locally compact groups). Moreover, if 픾 is of Kac type, we show that 픾 has property T if and only if every finite-dimensional irreducible *-representation of is an isolated point in the spectrum of (this also generalizes the corresponding locally compact group result). In addition, we give a way to construct property T discrete quantum groups using bicrossed products. [ABSTRACT FROM AUTHOR]