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Exceptional Symmetries

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Lie groups lie at the intersection of geometry and algebra, making them useful for many diverse areas of mathematics. As a representation theorist, I understand Lie groups by realizing them as symmetries of vector spaces–as automorphisms that respect some additional structure. In this talk I’ll discuss the construction and symmetries of two non-commutative algebras–the quaternions and the octonions. The quaternions naturally give insights into three- and four-dimensional geometry. The octonions are less easy to work with–they are not even associative. But we’ll see that they are the key to understanding the “exceptional” Lie groups, which don’t fall into any classical family.

This talk is part of the The Archimedeans (CU Mathematical Society) series.

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