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Clifford Algebras and Lie Theory - Eckhard Meinrenken
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2, ISBN: 9783642362163

ID: 203179783642362163

This monograph provides an introduction to the theory of Clifford algebras, with an emphasis on its connections with the theory of Lie groups and Lie algebras. The book starts with a detailed presentation of the main results on symmetric bilinear forms and Clifford algebras. It develops the spin groups and the spin representation, culminating in Cartan's famous triality automorphism for the group Spin(8). The discussion of enveloping algebras includes a presentation of Petracci's proof of the Po This monograph provides an introduction to the theory of Clifford algebras, with an emphasis on its connections with the theory of Lie groups and Lie algebras. The book starts with a detailed presentation of the main results on symmetric bilinear forms and Clifford algebras. It develops the spin groups and the spin representation, culminating in Cartan's famous triality automorphism for the group Spin(8). The discussion of enveloping algebras includes a presentation of Petracci's proof of the Poincaré-Birkhoff-Witt theorem. This is followed by discussions of Weil algebras, Chern-Weil theory, the quantum Weil algebra, and the cubic Dirac operator. The applications to Lie theory include Duflo's theorem for the case of quadratic Lie algebras, multiplets of representations, and Dirac induction. The last part of the book is an account of Kostant's structure theory of the Clifford algebra over a semisimple Lie algebra. It describes his "Clifford algebra analogue" of the Hopf-Koszul-Samelson theorem, and explains his fascinating conjecture relating the Harish-Chandra projection for Clifford algebras to the principal sl(2) subalgebra. Aside from these beautiful applications, the book will serve as a convenient and up-to-date reference for background material from Clifford theory, relevant for students and researchers in mathematics and physics. Group Theory, Mathematics, Clifford Algebras and Lie Theory~~ Eckhard Meinrenken~~Group Theory~~Mathematics~~9783642362163, en, Clifford Algebras and Lie Theory, Eckhard Meinrenken, 9783642362163, Springer, 02/28/2013, , , , Springer, 02/28/2013

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Clifford Algebras and Lie Theory - Eckhard Meinrenken
Vergriffenes Buch, derzeit bei uns nicht verfügbar.
(*)
Eckhard Meinrenken:
Clifford Algebras and Lie Theory - neues Buch

2013, ISBN: 9783642362163

ID: 689484272

This monograph provides an introduction to the theory of Clifford algebras, with an emphasis on its connections with the theory of Lie groups and Lie algebras. The book starts with a detailed presentation of the main results on symmetric bilinear forms and Clifford algebras. It develops the spin groups and the spin representation, culminating in Cartans famous triality automorphism for the group Spin(8). The discussion of enveloping algebras includes a presentation of Petraccis proof of the PoincaréBirkhoffWitt theorem.This is followed by discussions of Weil algebras, Chern--Weil theory, the quantum Weil algebra, and the cubic Dirac operator. The applications to Lie theory include Duflos theorem for the case of quadratic Lie algebras, multiplets of representations, and Dirac induction. The last part of the book is an account of Kostants structure theory of the Clifford algebra over a semisimple Lie algebra. It describes his Clifford algebra analogue of the HopfKoszulSamelson theorem, and explains his fascinating conjecture relating the Harish-Chandra projection for Clifford algebras to the principal sl(2) subalgebra.Aside from these beautiful applications, the book will serve as a convenient and up-to-date reference for background material from Clifford theory, relevant for students and researchers in mathematics and physics. This book covers the basics of Clifford algebras and spinor modules, with applications to the theory of Lie groups. Topics include Petracci’s proof of the Poincare-Birkhoff-Witt theorem, quantized Weil algebras, Duflo’s theorem for quadratic Lie algebras and more. eBooks > Fremdsprachige eBooks > Englische eBooks > Sach- & Fachthemen > Mathematik PDF 28.02.2013 eBook, .201, [PU: Springer, Berlin/Heidelberg/New York, NY]

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Clifford Algebras and Lie Theory - Eckhard Meinrenken
Vergriffenes Buch, derzeit bei uns nicht verfügbar.
(*)
Eckhard Meinrenken:
Clifford Algebras and Lie Theory - neues Buch

2013, ISBN: 9783642362163

ID: 689484272

This monograph provides an introduction to the theory of Clifford algebras, with an emphasis on its connections with the theory of Lie groups and Lie algebras. The book starts with a detailed presentation of the main results on symmetric bilinear forms and Clifford algebras. It develops the spin groups and the spin representation, culminating in Cartans famous triality automorphism for the group Spin(8). The discussion of enveloping algebras includes a presentation of Petraccis proof of the PoincaréBirkhoffWitt theorem.This is followed by discussions of Weil algebras, Chern--Weil theory, the quantum Weil algebra, and the cubic Dirac operator. The applications to Lie theory include Duflos theorem for the case of quadratic Lie algebras, multiplets of representations, and Dirac induction. The last part of the book is an account of Kostants structure theory of the Clifford algebra over a semisimple Lie algebra. It describes his Clifford algebra analogue of the HopfKoszulSamelson theorem, and explains his fascinating conjecture relating the Harish-Chandra projection for Clifford algebras to the principal sl(2) subalgebra.Aside from these beautiful applications, the book will serve as a convenient and up-to-date reference for background material from Clifford theory, relevant for students and researchers in mathematics and physics. This book covers the basics of Clifford algebras and spinor modules, with applications to the theory of Lie groups. Topics include Petracci’s proof of the Poincare-Birkhoff-Witt theorem, quantized Weil algebras, Duflo’s theorem for quadratic Lie algebras and more. eBooks > Fremdsprachige eBooks > Englische eBooks > Sach- & Fachthemen > Mathematik PDF 28.02.2013, .201, [PU: Springer, Berlin/Heidelberg/New York, NY]

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Clifford Algebras and Lie Theory: Eckhard Meinrenken Clifford Algebras and Lie Theory: Eckhard Meinrenken eBooks > Fachthemen & Wissenschaft > Mathematik, Springer Berlin Heidelberg

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Clifford Algebras and Lie Theory - Eckhard Meinrenken
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Eckhard Meinrenken:
Clifford Algebras and Lie Theory - neues Buch

2013, ISBN: 9783642362163

ID: 27755155

2013, eBook Download (PDF), eBooks, [PU: Springer Berlin]

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