Algebraic Groups and Discontinuous Subgroups by A. Borel, G. Mostow PDF

By A. Borel, G. Mostow

Show description

Read or Download Algebraic Groups and Discontinuous Subgroups PDF

Similar algebra books

Download e-book for kindle: Lineare Algebra und Analytische Geometrie in Fragen und by Doz. Dr. rer. nat. Karl-Heinz Gärtner, Dr. rer. nat. Roland

Dieses Buch mit seinen zahlreichen Fragen und Antworten sowie Aufgaben und Lösungen wendet sich vorwiegend an Studierende natur- und ingenieurwissenschaftlicher Studiengänge der ersten Semester an Technischen Universitäten und Fachhochschulen. Im Mittelpunkt stehen Vektoren, Determinanten und Matrizen, lineare Gleichungssysteme, Eigenwerte und Eigenvektoren quadratischer Matrizen, Gerade und Ebene im Raum, Verschiebung und Drehung von Koordinatensystemen, Kegelschnitte.

Extra resources for Algebraic Groups and Discontinuous Subgroups

Example text

E. In the former hence x _< b I ~ a 5 and and again B(a,b) a p case, and and the a ~ b _< D ( a A b) = D ( p ) p _< a I v a 3. Similarly a i _< a and the (b I v x) since separation property relation. Since transitivity of E) B(a,b) holds. holds. or Otherwise, an a t o m atoms M(L) has the e x - [0,a I ~ a 2 ~ b I v P ] L either we h a v e All (since (b I v b3) A (a I ~ a 2 ~ p) # 0 a I ~ a 2 ~ p _< a in we have p _< b I v b3, b i _< b. aI ~ a2 ~ bI ~ b 2 = aI ~ bI ~ p fails, a6 < p _< a A b p _< b 2 v b 4 are under property); bI E b3 since A (a I ~ a 2 ~ p) _> p # 0, bI E x (b 3 v x) an atom E = A fails b2 E x (a I ~ a 2 ~ p) # 0.

A v = I, 1 E J(L), then a v = i v = i_ E ~(L). 2. If (ii) k Proof. 1, ducts of non-void (ii) ~ (i) ~ [0} U [i} But (iv) follows The is a complete lattice. Moreover ~(L) U [0} U [i} if these and sums in L. from Lemma to show that ~(L) U [0} is closed under pro- ~ ~ S=J(L) U [0}. U[O}, [0}. in (1) c Immediate subsets. ScJ(L) (iii). is a complete Suppose a £ J ( L ) U ~O} U ~i}. a ~J(L)U of sets for are equivalent: (iii) J ( L ) U [O} U ~i} then ~products (ili) it suffices By hypothesis, course is maximal; are the same as in Lemma S~.

U[O}, [0}. in (1) c Immediate subsets. ScJ(L) (iii). is a complete Suppose a £ J ( L ) U ~O} U ~i}. a ~J(L)U of sets for are equivalent: (iii) J ( L ) U [O} U ~i} then ~products (ili) it suffices By hypothesis, course is maximal; are the same as in Lemma S~. L E ~r' then the following are satisfied ~(L) U [0} U [l} rings are maximal. 1. then U~O}. (iii) ~ Let S = ~IJ If from Lemma a=NS. 2. 59 6. THE CASE THAT J(L) We note that for complete lattice AND ~(L) LE2r ARE COMPLETE LATTICES FOR the condition that algebra.

Download PDF sample

Algebraic Groups and Discontinuous Subgroups by A. Borel, G. Mostow


by Joseph
4.3

Rated 4.21 of 5 – based on 9 votes