# Clifford algebra and multidimensional function theory

Course Code : | 2002WETCAD |

Study domain: | Mathematics |

Academic year: | 2017-2018 |

Semester: | 2nd semester |

Contact hours: | 60 |

Credits: | 6 |

Study load (hours): | 168 |

Contract restrictions: | No contract restriction |

Language of instruction: | Dutch |

Exam period: | exam in the 2nd semester |

Lecturer(s) | David Eelbode |

### 1. Prerequisites *

an active knowledge of

- Dutch

- English

specific prerequisites for this coursePossible seminars and extra material in the form of research papers will mostly be presented in English.

*General competences

Students are required to be familiar with elementary notions from complex analysis and group theory.

Sequentiality:

Complexe analysis and Riemann-surfaces (3BWIS-A-08)

### 2. Learning outcomes *

- * the student is familiar with the topics on multi-dimensional analysis and the theory of Clifford algebras treated throughout the course
- * the student is able to reproduce the theorems from the course notes and can illustrate the reasoning behind them
- * the student is able to use the theorems and properties to solve exercises of theoretical nature in which a combination of material from the course notes leads to the correct answer
- * the student is able to explain in what sense certain generalisations of theorems and results from classical and complex analysis are indeed analogues

### 3. Course contents *

The following notions will be treated during the classes:

* Clifford algebras (and their classification)

* spinor representations for the orthogonal Lie algebra

* the spin group and its link with the orthogonal Lie group

* the Dirac operator in Clifford analysis

* (simplicial) monogenic functions and their relation to harmonic functions

* Howe dualities for harmonic and monogenic functions

Further topics will be determined based on the interest of the sudents.

### 4 International dimension*

### 5. Teaching method and planned learning activities

### 6. Assessment method and criteria

### 7. Study material *

#### 7.1 Required reading

Course notes will be available (Dutch), and additional material in the form of papers (English)

**7.2 Optional reading**

The following study material can be studied voluntarily :Brackx, F., Delanghe, R., Sommen, F., Clifford Analysis, Research Notes in Mathematics 76, Pitman, London (1982).

Delanghe, R., Sommen, F., Soucek, V., Clifford analysis and spinor valued functions, Kluwer Academic Publishers, Dordrecht (1992).

Gilbert, J., Murray, M.A.M., Clifford algebras and Dirac operators in harmonic analysis, Cambridge University Press, Cambridge (1991).

### 8. Contact information *

David Eelbode: david.eelbode@gmail.com (G.312)