exceptional structures, exceptional isomorphisms
exceptional finite rotation groups:
and Kac-Moody groups:
Various kinds of (mathematical) structures have classifications by which the possible examples/cases of these structures are elements either
of some infinite sequence of such structures, following some systematic construction rule,
or else of a (typically finite) set of examples which follow no such rule.
In the second case, these “unsystematic” examples of the given kind of structure are then often called exceptional or sporadic.
Exceptional structures are often related to one another. For example, the exceptional Lie group G2 is the symmetry group of the octonions, and the other exceptional Lie groups are related to the octonions in the Freudenthal magic square, while the Albert algebra is the exceptional Jordan algebra of 3-by-3 hermitian matrices over the octonions. The Leech lattice is related to the Monster simple group, and can also be connected with the octonions (Wilson 09). Moreover, all these structures tend to appear as aspects of M-theory.
exceptional structures, exceptional isomorphisms
exceptional finite rotation groups:
and Kac-Moody groups:
See also
Wikipedia, Exceptional object
Yang-Hui He, John McKay, Sporadic and Exceptional, (arXiv:1505.06742)
Robert A. Wilson, Octonions and the Leech lattice, Journal of Algebra
Volume 322, Issue 6, 15 September 2009, Pages 2186-2190, (pdf), (slides)
Piero Truini, Michael Rios, Alessio Marrani, The Magic Star of Exceptional Periodicity (arXiv:1711.07881)
Michael Rios, Alessio Marrani, David Chester, Exceptional Super Yang-Mills in $D=27+3$ and Worldvolume M-Theory (arXiv:1906.10709)
Last revised on June 27, 2019 at 06:55:58. See the history of this page for a list of all contributions to it.