5 edition of **Clifford theory for group representations** found in the catalog.

- 221 Want to read
- 36 Currently reading

Published
**1989**
by North-Holland, Sole distributors for the U.S.A. and Canada, Elsevier Science Pub. Co. in Amsterdam, New York, New York, N.Y., U.S.A
.

Written in English

- Clifford algebras.,
- Representations of groups.

**Edition Notes**

Statement | Gregory Karpilovsky. |

Series | North-Holland mathematics studies ;, 156, Notas de matemática ;, 125, Notas de matemática (Rio de Janeiro, Brazil) ;, no. 125. |

Classifications | |
---|---|

LC Classifications | QA1 .N86 no. 125, QA199 .N86 no. 125 |

The Physical Object | |

Pagination | x, 364 p. ; |

Number of Pages | 364 |

ID Numbers | |

Open Library | OL2185296M |

ISBN 10 | 0444873775 |

LC Control Number | 89003233 |

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 : Eckhard Meinrenken. 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.

"Zee's lovely book on the theory of group representations is comprehensive and complete, both from the mathematical and physical points of view. While it doesn't discuss the representations of the symmetric groups, the book's got almost everything on the mathematical side, including roots and weights in the theory of compact Lie groups. Main Clifford algebras and Lie theory. Clifford algebras and Lie theory Eckhard Meinrenken. representations define decomposition bracket enveloping det filtration reductive lie Post a Review You can write a book review and share your experiences. Other readers will always be interested in your opinion of the.

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. If N is odd, there are two such representations, each of degree 2^((N-1)/2). Roughly, all this means: The CLIFFORD ALGEBRA is the GROUP ALGEBRA of the DISCRETE CLIFFORD GROUP. The Discrete Clifford Group contains many of the properties of the Clifford Algebra, including, as shown by Boya and Byrd, the 8-fold Periodicity Property.

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Additional Physical Format: Online version: Karpilovsky, Gregory, Clifford theory for group representations.

Amsterdam ; New York: North-Holland ; New York, N.Y. This short chapter introduces Clifford theory, which is the subject of comparing the representation theories of a finite group and a normal subgroup of it. We prove Clifford’s theorem in the first section.

The rest of the chapter discusses how to go from the representations of the normal subgroup and the quotient to representations of the group. Clifford Theory for Group Representations Gregory Karpilovsky. Let N be a normal subgroup of a finite group G and let F be a field. An important method for constructing irreducible FG-modules consists of the application (perhaps repeated) of three basic operations: (i) restriction to FN.

You can write a book review and share your. In mathematics, a Clifford algebra is an algebra generated by a vector space with Clifford theory for group representations book quadratic form, and is a unital associative K-algebras, they generalize the real numbers, complex numbers, quaternions and several other hypercomplex number systems.

The theory of Clifford algebras is intimately connected with the theory of quadratic forms and orthogonal transformations.

Purchase Clifford Theory for Group Representations, Volume - 1st Edition. Print Book & E-Book. ISBNPages: Get this from a library. Clifford theory for group representations. [Gregory Karpilovsky] -- Let N be a normal subgroup of a finite group G and let F be a field.

An important method for constructing irreducible FG-modules consists of the application (perhaps repeated) of three basic. Search in this book series. Clifford Theory for Group Representations. Edited by Leopoldo Nachbin, Gregory Karpilovsky.

VolumePages ii-viii, () Download full volume. Previous volume. Next volume. Actions for selected chapters.

Select all / Deselect all. Download PDFs Export citations. thereby giving representations of the group on the homology groups of the space.

If there is torsion in the homology these representations require something other than ordinary character theory to be understood. This book is written for students who are studying nite group representation theory beyond the level of a rst course in abstract Size: 1MB.

This book is a unique survey of the whole field of modular representation theory of finite groups. The main topics are block theory and module theory of group representations, including blocks with cyclic defect groups, symmetric groups, groups of Lie type, local-global conjectures.

This volume contains a concise exposition of the theory of finite groups, including the theory of modular representations. The rudiments of linear algebra and knowledge of the elementary concepts of group theory are useful, if not entirely indispensable, prerequisites for reading this book; most of the other requisites, such as the theory of p-adic fields, are developed in the by: Let N be a normal subgroup of a finite group G and let F be a field.

An important method for constructing irreducible FG-modules consists of the application, ISBN Buy the Clifford Theory for Group Representations ebook. This book does finite group representation theory and goes quite in depth with it (including some mention of the case where Maschke's theorem does not hold).

I believe it is intended for a graduate course but I personally feel like it is a book an undergraduate can also grow into. 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 : Springer-Verlag Berlin Heidelberg. Clifford Theory for Group Representations Leopoldo Nachbin and Gregory Karpilovsky (Eds.) (iii) induction from FN.

This is the `Clifford Theory' developed by Clifford in In the past twenty years, the theory has enjoyed a period of vigorous development. The foundations have been strengthened and reorganized from new points of view.

Clifford groups and representations Rotations on the vector space \({V}\), i.e. linear transformations that preserve the inner product, can be expressed in terms of Clifford multiplication, regardless of.

“This book is intended as a text for first year master students who want to specialize on representation theory, more precisely: representations of finite-dimensional algebras and modular group representations, with special emphasis on homological methods.” (Wolfgang Rump, zbMATH)Cited by: 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. the rst few spin groups, the ones that behave in a non-generic way. Spin(2) is a circle, double-covering the circle SO(2). Spin(3) = SU(2) = Sp(1), and the spin representation is the fundamental representation of SU(2).

The Dynkin diagram is a single isolated node. Spin(4) = SU(2) SU(2), and the half-spin representations are the funda-File Size: KB. precise classi cation of representations of compact Lie groups, through the theory of highest weight representations, is not considered beyond the case of SU 2pCq; this is however covered in great detail in many other texts, such as [20] again, the book [37] of Knapp (especially Chapter V), or the book [35] of Kirillov.

Size: 1MB. Representations and spinors With the matrix isomorphisms of the previous section in hand, the representation theory of Clifford algebras is quite simple, although the terminology is less so due to historical artifacts.

This is an introduction to Clifford theory of induced representations from normal subgroups of finite groups. As an application, a complete explicit description of the irreducible representations.You can write a book review and share your experiences. Other readers will always be interested in your opinion of the books you've read.

Whether you've loved the book or not, if you give your honest and detailed thoughts then people will find new books that are right for them. Brauer and Weyl, inwere the first to systematize these spin representations in terms of the language of Clifford algebras, but it was Chevalley in his classic monograph, The Algebraic Theory of Spinors and Clifford Algebras (Columbia University Press,reprinted by Springer in as Vol.

2 of his Collected Works), who gave a.