### Abstract

The derivation constant K(A) ≥ 1 2 has been extensively studied for unital noncommutative C ∗ -algebras. In this paper, we investigate properties of K(M(A)) where M(A) is the multiplier algebra of a non-unital C ∗ -algebra A. A number of general results are obtained which are then applied to the group C ∗ -algebras A = C ∗ (GN ) where GN is the motion group R N o SO(N). Utilising the rich topological structure of the unitary dual GdN , it is shown that, for N ≥ 3, K(M(C ∗ (GN ))) = 1 2 ⌈ N 2 ⌉

Original language | English |
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Pages (from-to) | 225-255 |

Number of pages | 31 |

Journal | Advances in Mathematics |

Volume | 280 |

Early online date | 15 May 2015 |

DOIs | |

Publication status | Published - 6 Aug 2015 |

### Keywords

- C∗-algebra
- multiplier algebra
- derivation
- motion group
- unitary dual
- graph structure

## Fingerprint Dive into the research topics of 'Norms of inner derivations for multiplier algebras of C ∗ -algebras and group C ∗ -algebras, II'. Together they form a unique fingerprint.

## Profiles

### Robert Archbold

- School of Natural & Computing Sciences, Mathematical Science - Emeritus Professor

Person: Honorary

## Cite this

Archbold, R. J., Kaniuth, E., & Somerset, D. W. B. (2015). Norms of inner derivations for multiplier algebras of C ∗ -algebras and group C ∗ -algebras, II.

*Advances in Mathematics*,*280*, 225-255. https://doi.org/10.1016/j.aim.2015.04.019