Download An Account of the Theory of Crystallographic Groups by Louis Auslander PDF

By Louis Auslander

Complaints of the yank Mathematical Society
Vol. sixteen, No. 6 (Dec., 1965), pp. 1230-1236
Published via: American Mathematical Society
DOI: 10.2307/2035904
Stable URL: http://www.jstor.org/stable/2035904
Page count number: 7

Show description

Read Online or Download An Account of the Theory of Crystallographic Groups PDF

Best group theory books

Groups and Symmetry: A Guide to Discovering Mathematics (Mathematical World, Volume 5)

In such a lot arithmetic textbooks, the main intriguing a part of mathematics--the means of invention and discovery--is thoroughly hidden from the reader. the purpose of teams and Symmetry is to alter all that. by way of a chain of rigorously chosen initiatives, this booklet leads readers to find a few genuine arithmetic.

Groups of Finite Morley Rank

This e-book basically info the speculation of teams of finite Morley rank--groups which come up in version concept and generalize the concept that of algebraic teams over algebraically closed fields. Written specifically for natural staff theorists and graduate scholars embarking on examine at the topic, the e-book develops the idea from the start and includes an algebraic and self-evident instead of a model-theoretic perspective.

Additional resources for An Account of the Theory of Crystallographic Groups

Example text

So y(E) leaves this subspace invariant, the f u l l s t a b i l i z er being a proper parabolic subgroup of L<|_*. Taking preimages under 4> we obtain a proper parabolic subgroup of Py containing E. As above, E is contained in a Levi f a c t o r of this parabolic subgroup, and this contradicts m i n i m a l i t y of Py. So the claim holds. We have now established the existence of a parabolic subgroup 34 GARYM. SEITZ Py satisfying (1), (11), and (iii). For uniqueness we use the fact that for a given Levi factor Ly of Py there are only two parabolic subgroups of Y with Levi factor equal to Ly-namely Py and its opposite.

I i ) . ® (V1 ^ 1 (Q)) r d. Proof. 6). The next several results are technical but Important as they link the group theory and the representation theory. The f i r s t result shows one can usually choose Py so that r | Z = cc|Z f o r each r € Tr(Y)-TT(l_Y). A consequence w i l l be that in most cases V|X i s a basic module, although this w i l l not be proved until §10. 6). Assume Y is a classical group w i t h natural module W and W|X is an irreducible basic or p-basic module. Then Py can be chosen so that the followin g hold: (i).

P r o o f . 4) Qy ^ contains an L y - c o m p o s i t i o n factor isomorphic to I ^ , f o r some q. 4)(iv) shows such a composition facto r exists which is covered by Q. 4)(iii) j ^ | T = -cc. Therefore, q = 1. ,Df be the L'-composition f a c t o r s of V L . ( - r ) . (-r)lL')(S)D( < for some k. Decompose D[< into a tensor product of t w i s t s of r e s t r i c t e d modules, consider high weights, and obtain the result. 10). 9) and M£ is t r i v i a l for MAXIMAL SUBGROUPS OF CLASSICAL GROUPS each £ ^ i w i t h L# adjoining r.

Download PDF sample

An Account of the Theory of Crystallographic Groups by Louis Auslander


by Michael
4.4

Rated 4.82 of 5 – based on 47 votes