Full Record

Author | Laubacher, Jacob C |

Title | Secondary Hochschild and Cyclic (Co)homologies |

URL | http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1489422065908758 |

Publication Date | 2017 |

Degree | PhD |

Discipline/Department | Mathematics |

Degree Level | doctoral |

University/Publisher | Bowling Green State University |

Abstract | Hochschild cohomology was originally introduced in 1945. Much more recently in 2013 a generalization of this theory, the secondary Hochschild cohomology, was brought to light. In this dissertation we provide the details behind the simplicial structure for the chain complexes associated to the (secondary) Hochschild (co)homology. For this we introduce the notion of simplicial algebras and simplicial modules. The key results are two lemmas (3.4.1 and 3.4.2) that can be thought of as analogues of the Tor and Ext functors in the context of simplicial modules. It was a pleasant surprise that the higher order Hochschild homology over the 2-sphere can also be described using simplicial structures. We study some other related concepts like the secondary Hochschild and cyclic homologies associated to the triple (A,B,ε), as well as some of their properties. |

Subjects/Keywords | Mathematics; homological algebra; deformation theory; associative rings and algebras; Hochschild cohomology; cyclic cohomology |

Contributors | Staic, Mihai D. (Advisor) |

Language | en |

Rights | unrestricted ; This thesis or dissertation is protected by copyright: all rights reserved. It may not be copied or redistributed beyond the terms of applicable copyright laws. |

Country of Publication | us |

Format | application/pdf |

Record ID | oai:etd.ohiolink.edu:bgsu1489422065908758 |

Repository | ohiolink |

Date Indexed | 2020-10-19 |

Grantor | Bowling Green State University |