By Eckhard Meinrenken
This monograph offers an advent to the speculation of Clifford algebras, with an emphasis on its connections with the speculation of Lie teams and Lie algebras. The e-book starts off with an in depth presentation of the most effects on symmetric bilinear types and Clifford algebras. It develops the spin teams and the spin illustration, culminating in Cartan’s recognized triality automorphism for the crowd Spin(8). The dialogue of enveloping algebras encompasses a presentation of Petracci’s facts of the Poincaré–Birkhoff–Witt theorem.
This is via discussions of Weil algebras, Chern--Weil concept, the quantum Weil algebra, and the cubic Dirac operator. The purposes to Lie concept comprise Duflo’s theorem for the case of quadratic Lie algebras, multiplets of representations, and Dirac induction. The final a part of the booklet is an account of Kostant’s constitution thought of the Clifford algebra over a semisimple Lie algebra. It describes his “Clifford algebra analogue” of the Hopf–Koszul–Samelson theorem, and explains his interesting conjecture referring to the Harish-Chandra projection for Clifford algebras to the crucial sl(2) subalgebra.
Aside from those attractive functions, the booklet will function a handy and updated reference for history fabric from Clifford concept, appropriate for college students and researchers in arithmetic and physics.
Read Online or Download Clifford Algebras and Lie Theory: 58 (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics) PDF
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Extra resources for Clifford Algebras and Lie Theory: 58 (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics)
Clifford Algebras and Lie Theory: 58 (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics) by Eckhard Meinrenken
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