On a Grading of the Cuntz Algebra

Abstract

© 2019, Pleiades Publishing, Ltd. In the paper we introduce the notion of a local group and define a Fell bundle over a local group and a *-representation of a local group into a C*-algebra. We show that with every partial representation of a group the local group is connected as well as the respective Fell bundle. Also we show that the Cuntz and the Cuntz-Toeplitz algebras are local group graded.