GAMABC.COM.UA Book Archive

Group Theory

Download A Course in Finite Group Representation Theory by Peter Webb PDF

By Peter Webb

This graduate-level textual content offers an intensive grounding within the illustration concept of finite teams over fields and earrings. The e-book offers a balanced and entire account of the topic, detailing the tools had to examine representations that come up in lots of components of arithmetic. Key subject matters contain the development and use of personality tables, the function of induction and limit, projective and straightforward modules for workforce algebras, indecomposable representations, Brauer characters, and block concept. This classroom-tested textual content presents motivation via a good number of labored examples, with workouts on the finish of every bankruptcy that attempt the reader's wisdom, offer additional examples and perform, and comprise effects no longer confirmed within the textual content. necessities comprise a graduate path in summary algebra, and familiarity with the houses of teams, earrings, box extensions, and linear algebra.

Show description

Read or Download A Course in Finite Group Representation Theory PDF

Similar group theory books

Elements of the History of Mathematics

This paintings gathers jointly, with no tremendous amendment, the major­ ity of the ancient Notes that have looked as if it would date in my components de M atMmatique. simply the circulation has been made self sufficient of the weather to which those Notes have been hooked up; they're for this reason, in precept, available to each reader who possesses a valid classical mathematical heritage, of undergraduate commonplace.

Intégration: Chapitre 6

Les ? ‰l? ©ments de math? ©matique de Nicolas Bourbaki ont pour objet une pr? ©sentation rigoureuse, syst? ©matique et sans pr? ©requis des math? ©matiques depuis leurs fondements. Ce sixi? ?me chaptire du Livre d Int? ©gration, sixi? ?me Livre des ? ©l? ©ments de math? ©matique, ? ©tend l. a. concept d int?

Moduln mit einem höchsten Gewicht

Booklet by way of Jantzen, Jens C.

Classical Artinian Rings and Related Topics

Quasi-Frobenius jewelry and Nakayama jewelry have been brought via T Nakayama in 1939. due to the fact then, those classical artinian earrings have endured to fascinate ring theorists with their abundance of homes and structural intensity. In 1978, M Harada brought a brand new classification of artinian earrings that have been later known as Harada earrings in his honour.

Extra info for A Course in Finite Group Representation Theory

Sample text

An element e of a ring A is said to be idempotent if e2 = e. It is a central idempotent element if it lies in the center Z(A). Two idempotent elements e and f are orthogonal if ef = f e = 0. An idempotent element e is called primitive if whenever e = e1 + e2 where e1 and e2 are orthogonal idempotent elements then either e1 = 0 or e2 = 0. We say that e is a primitive central idempotent element if it is primitive as an idempotent element in Z(A), that is, e is central and has no proper decomposition as a sum of orthogonal central idempotent elements.

Without this exponent we would get a right RG-module. If R happens to be a field and we have bases v1 , . . , vm for V and w1 , . . , wn for W then V ⊗ W has a basis {vi ⊗ wj 1 ≤ i ≤ m, 1 ≤ j ≤ n} and V ∗ has a dual basis CHAPTER 3. CHARACTERS 26 vˆ1 , . . , vˆm . With respect to these bases an element g ∈ G acts on V ⊗ W with the matrix that is the tensor product of the two matrices giving its action on V and W , and on V ∗ it acts with the transpose of the inverse of the matrix of its action on V .

In particular ni is determined by V independently of the choice of decomposition. 2. Let G = S3 and denote by C the trivial representation, the sign representation and V the 2-dimensional simple representation over C. We decompose the 4-dimensional representation V ⊗V as a direct sum of simple representations. Since the values of the character χV give the row of the character table χV 2 0 −1 CHAPTER 3. CHARACTERS 31 we see that V ⊗ V has character values χV ⊗V Thus 4 0 1 1 χV ⊗V , χC = (4 · 1 + 0 + 2 · 1 · 1) = 1 6 1 χV ⊗V , χ = (4 · 1 + 0 + 2 · 1 · 1) = 1 6 1 χV ⊗V , χV = (4 · 2 + 0 − 2 · 1 · 1) = 1 6 and we deduce that V ⊗V ∼ = C ⊕ ⊕ V.

Download PDF sample

A Course in Finite Group Representation Theory by Peter Webb


by Ronald
4.4

Rated 4.85 of 5 – based on 50 votes