### 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 |
---|---|

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 |

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### Keywords

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

### Cite this

*Advances in Mathematics*,

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

**Norms of inner derivations for multiplier algebras of C ∗ -algebras and group C ∗ -algebras, II.** / Archbold, Robert J; Kaniuth, Eberhard; Somerset, Douglas W B.

Research output: Contribution to journal › Article

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

}

TY - JOUR

T1 - Norms of inner derivations for multiplier algebras of C ∗ -algebras and group C ∗ -algebras, II

AU - Archbold, Robert J

AU - Kaniuth, Eberhard

AU - Somerset, Douglas W B

PY - 2015/8/6

Y1 - 2015/8/6

N2 - 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 ⌉

AB - 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 ⌉

KW - C∗-algebra

KW - multiplier algebra

KW - derivation

KW - motion group

KW - unitary dual

KW - graph structure

U2 - 10.1016/j.aim.2015.04.019

DO - 10.1016/j.aim.2015.04.019

M3 - Article

VL - 280

SP - 225

EP - 255

JO - Advances in Mathematics

JF - Advances in Mathematics

SN - 0001-8708

ER -