Lectures on Exceptional Lie Groups
University of Chicago Press, 1996 - 122 pages
J. Frank Adams was internationally known and respected as one of the great algebraic topologists. Adams had long been fascinated with exceptional Lie groups, about which he published several papers, and he gave a series of lectures on the topic. The author's detailed lecture notes have enabled volume editors Zafer Mahmud and Mamoru Mimura to preserve the substance and character of Adams's work.
Because Lie groups form a staple of most mathematics graduate students' diets, this work on exceptional Lie groups should appeal to many of them, as well as to researchers of algebraic geometry and topology.
J. Frank Adams was Lowndean professor of astronomy and geometry at the University of Cambridge. The University of Chicago Press published his Lectures on Lie Groups and has reprinted his Stable Homotopy and Generalized Homology.
Chicago Lectures in Mathematics Series
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0-eigenspace 1-dimensional 2AoB A2BA ABA2 action of F4 acts on Rn Addendum algebra of polynomial alternating function associative algebra attain maximum distance Cayley line Cayley projective plane Claim collinear conjugate Corollary 15.5 corresponding db,da determined diagonal matrices dimension 16 eigenspace of dimension element of F4 element of Spin(9 exceptional Jordan algebra F4 act F4-orbit finishes the proof Hermitian idempotent identify ij are orthonormal Im(xy Im(yx imaginary Cayley numbers invariant under F4 isometry isomorphic Jordan algebras Definition k(ij linear map normed algebra numbers x orbit orthogonal complement orthogonal to H orthonormal basis polarise polynomial functions preserve the inner preserves inner products products and f proof of Theorem Proof.(i Proposition 16.4 pure imaginary Cayley Re(x(yz Re(xy Re(yx Rp_1 set in Lemma special Jordan algebra subalgebra subgroup of Aut(J subspace symmetric treatment of F4 trilinear function vector space x,yz x(yy X2 Xi A3 xx)y xy,z xy)y xy)z