# H * -algebra

## 0.1 H *-algebra

An *H $\mathrm{*}$-algebra* is defined as a Hilbert space^{} ${\mathbb{A}}_{H}$ equipped with an associative unital algebra structure^{} and an antilinear involution^{} ${}^{*}:{\mathbb{A}}_{H}\to {\mathbb{A}}_{H}$ which is compatible^{} with taking the adjoint^{} of the operators on the Hilbert space for the left and right multiplication of ${\mathbb{A}}_{H}$ with itself (ref. [1]).

## References

- 1 Baez, J. 2007. http://golem.ph.utexas.edu/category/2006/10/categorified_gelfandnaimark_th.htmlGroupoidification. (Preprint)

Title | H * -algebra |

Canonical name | Halgebra |

Date of creation | 2013-03-22 18:26:32 |

Last modified on | 2013-03-22 18:26:32 |

Owner | bci1 (20947) |

Last modified by | bci1 (20947) |

Numerical id | 7 |

Author | bci1 (20947) |

Entry type | Definition |

Classification | msc 20G42 |

Classification | msc 81R05 |

Classification | msc 81R15 |

Classification | msc 46N50 |

Related topic | HilbertSpace |

Related topic | QuantumSpaceTimes |

Related topic | VonNeumannAlgebra |

Related topic | WeakHopfCAlgebra2 |

Related topic | CategoryOfHAlgebras |