Rocky Mountain Journal of Mathematics

Partial group algebra with projections and relations

Danilo Royer

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


We introduce the notion of the partial group algebra with projections and relations and show that this $C^*$-algebra is a partial crossed product. Examples of partial group algebras with projections and relations are the Cuntz-Krieger algebras and the unitization of $C^*$-algebras of directed graphs.

Article information

Rocky Mountain J. Math., Volume 49, Number 2 (2019), 645-660.

Received: 29 March 2018
Revised: 8 August 2018
First available in Project Euclid: 23 June 2019

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46L05: General theory of $C^*$-algebras

partial group algebra partial crossed product


Royer, Danilo. Partial group algebra with projections and relations. Rocky Mountain J. Math. 49 (2019), no. 2, 645--660. doi:10.1216/RMJ-2019-49-2-645.

Export citation


  • \labelexelcircleactions R. Exel, Circle actions on $C^*$-algebras, partial automorphisms and a generalized Pimsner-Voiculescu exact sequence, Funct. Anal. 122 (1994), 361–401.
  • \labelamenabilityforfell ––––, Amenability for Fell bundles, J. reine angew. Math. 492 (1997), 41–73.
  • \labelexelpartrep ––––, Partial actions of groups and actions of inverse semigroups, Proc. Amer. Math. Soc. 126 (1998), 3481–3494.
  • \labelexelpartrepamenable ––––, Partial representations and amenable Fell bundles over free groups, Pacific J. Math. 192 (2000), 39–63.
  • \labelexelquigglaca R. Exel, M. Laca and J. Quigg, Partial dynamical systems and $C^*$-algebras generated by partial isometries, J. Oper. Th. 47 (2002), 169–186.
  • \labelgraphalgebraslaca N.J. Fowler, M. Laca and I. Raeburn, The $C^*$-algebras of infinite graphs, Proc. Amer. Math. Soc. 128 (1999), 2319–2327.
  • \labelmclanahan K. McClanahan, $K$-theory for partial actions by discrete groups, J. Funct. Anal. 130 (1995), 77–117.
  • \labelraeburn I. Raeburn, Graph algebras, CBMS Reg. Conf. Ser. Math. 103 (2004).