Pertti LounestoMy research focuses on algebras emerging from problems in geometry and physics, called Clifford algebras. In physics, the concept of Clifford algebra, as such or in a disguise, is a necessity in the description of electron spin, because spinors cannot be constructed by tensorial methods, in terms of exterior powers of the vector space. In geometry, information about orientation of subspaces can be encoded in simple multivectors, which can be added and multiplied. Physicists are familiar with this tool in the special case of one-dimensional subspaces, which they manipulate by vectors (not by projection operators, which lose information about orientations).I am also interested in misconceptions of research mathematicians, while they enter unexplored domains. This Spring 2002, I delivered lectures on Clifford algebras. |
Pertti Lounesto: Clifford Algebras and Spinors, Cambridge University Press, 1997, 306 pages. Second edition, 2001, 338 pages. Changes between editions 1/2. Reviews in English, German. |
Rafal Ablamowicz, Pertti Lounesto, Josep Parra (eds.): Clifford Algebras with Numeric and Symbolic Computations, Birkhäuser, 1996, 322 pages. Software to accompany the book. Review by Dongming Wang. |
Marcel Riesz (lecture notes, delivered in 1957-58), E. Folke Bolinder, Pertti Lounesto (eds.): Clifford Numbers and Spinors; with Riesz's private lectures to E. Folke Bolinder and a historical review by Pertti Lounesto, Kluwer, 1993, 241 pages. Review by S. Rogosin. |
Rafal Ablamowicz, Pertti Lounesto (eds.): Clifford Algebras and Spinor Structures: A special volume dedicated to the memory of Albert Crumeyrolle (1919-1992), Kluwer, 1995, 421 pages. |
Pertti Lounesto, Risto Mikkola, Vesa Vierros: CLICAL User Manual: Complex Number, Vector Space and Clifford Algebra Calculator for MS-DOS Personal Computers, Institute of Mathematics, Helsinki University of Technology, 1987, 80 pages. CLICAL is free to download. |
See errata of the books. See commentary of a paper, where the authors prove a conjecture of one of the above authors, although the conjecture was a corollory of Ado's theorem.
Hamilton's quaternions are used to represent 3D rotations; quaternions enable smooth interpolation of rotation matrices in computer graphics/ games, quaternions are used to avoid a singularity, the gimbal lock in flight simulation and spacecraft navigation.
W.R. Hamilton | H. Grassmann | W.K. Clifford | R. Lipschitz | E. Cartan | E. Witt | C. Chevalley | M. Riesz | J. Helmstetter |
Pertti.Lounesto@helsinka.fa (a -> i for e-mail) Department of Mathematics University of Helsinki FIN-00014 Helsinki, Finland |
My Erdös number is 3. |