### Abstract

We interpret the element 1/2ih (u * v + v * u) in the generators u, v of the Wey1 algebra W^{2} as an indeterminate in N+ 1/2 or -(N+ 1/2), using methods of the transcendental calculus outlined in the announcement [13]. The main purpose of this paper is to give a rigorous proof for the part of [13] which introduces this indeterminate phenomenon. Namely, we discuss how to obtain associativity in the transcendental calculus and show how the Hadamard finite part procedure can be implemented in our context.

Original language | English |
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Title of host publication | Differential Geometry, Mathematical Physics, Mathematics and Society Part 1 |

Pages | 267-297 |

Number of pages | 31 |

Edition | 321 |

Publication status | Published - 2008 Oct 1 |

Externally published | Yes |

### Publication series

Name | Asterisque |
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Number | 321 |

ISSN (Print) | 0303-1179 |

### Keywords

- Transcendental calculus
- Weyl algebra

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Omori, H., Maeda, Y., Miyazaki, N., & Yoshioka, A. (2008). A new nonformal noncommutative calculus: Associativity and finite part regularization. In

*Differential Geometry, Mathematical Physics, Mathematics and Society Part 1*(321 ed., pp. 267-297). (Asterisque; No. 321).