Clifford Algebras and Lie Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Clifford Algebras and Lie Theory write by Eckhard Meinrenken. This book was released on 2013-02-28. Clifford Algebras and Lie Theory available in PDF, EPUB and Kindle. 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.
Quadratic Algebras, Clifford Algebras, and Arithmetic Witt Groups
Quadratic Algebras, Clifford Algebras, and Arithmetic Witt Groups - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Quadratic Algebras, Clifford Algebras, and Arithmetic Witt Groups write by Alexander J. Hahn. This book was released on 2012-12-06. Quadratic Algebras, Clifford Algebras, and Arithmetic Witt Groups available in PDF, EPUB and Kindle. Quadratic Algebras, Clifford Algebras, and Arithmetic Forms introduces mathematicians to the large and dynamic area of algebras and forms over commutative rings. The book begins very elementary and progresses gradually in its degree of difficulty. Topics include the connection between quadratic algebras, Clifford algebras and quadratic forms, Brauer groups, the matrix theory of Clifford algebras over fields, Witt groups of quadratic and symmetric bilinear forms. Some of the new results included by the author concern the representation of Clifford algebras, the structure of Arf algebra in the free case, connections between the group of isomorphic classes of finitely generated projectives of rank one and arithmetic results about the quadratic Witt group.
Clifford Algebra to Geometric Calculus
Clifford Algebra to Geometric Calculus - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Clifford Algebra to Geometric Calculus write by David Hestenes. This book was released on 1984. Clifford Algebra to Geometric Calculus available in PDF, EPUB and Kindle. Matrix algebra has been called "the arithmetic of higher mathematics" [Be]. We think the basis for a better arithmetic has long been available, but its versatility has hardly been appreciated, and it has not yet been integrated into the mainstream of mathematics. We refer to the system commonly called 'Clifford Algebra', though we prefer the name 'Geometric Algebra' suggested by Clifford himself. Many distinct algebraic systems have been adapted or developed to express geometric relations and describe geometric structures. Especially notable are those algebras which have been used for this purpose in physics, in particular, the system of complex numbers, the quaternions, matrix algebra, vector, tensor and spinor algebras and the algebra of differential forms. Each of these geometric algebras has some significant advantage over the others in certain applications, so no one of them provides an adequate algebraic structure for all purposes of geometry and physics. At the same time, the algebras overlap considerably, so they provide several different mathematical representations for individual geometrical or physical ideas.
Clifford Algebras and the Classical Groups
Clifford Algebras and the Classical Groups - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Clifford Algebras and the Classical Groups write by Ian R. Porteous. This book was released on 1995-10-05. Clifford Algebras and the Classical Groups available in PDF, EPUB and Kindle. The Clifford algebras of real quadratic forms and their complexifications are studied here in detail, and those parts which are immediately relevant to theoretical physics are seen in the proper broad context. Central to the work is the classification of the conjugation and reversion anti-involutions that arise naturally in the theory. It is of interest that all the classical groups play essential roles in this classification. Other features include detailed sections on conformal groups, the eight-dimensional non-associative Cayley algebra, its automorphism group, the exceptional Lie group G(subscript 2), and the triality automorphism of Spin 8. The book is designed to be suitable for the last year of an undergraduate course or the first year of a postgraduate course.
An Introduction to Clifford Algebras and Spinors
An Introduction to Clifford Algebras and Spinors - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook An Introduction to Clifford Algebras and Spinors write by Jayme Vaz Jr.. This book was released on 2016. An Introduction to Clifford Algebras and Spinors available in PDF, EPUB and Kindle. This work is unique compared to the existing literature. It is very didactical and accessible to both students and researchers, without neglecting the formal character and the deep algebraic completeness of the topic along with its physical applications.
