J. Dieudonn'e, La G'eometrie des Groupes Classiques, Springer, Berlin, 1963. Home/Search Document Not in Database Summary Related Articles Check |
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Finite geometry after Aschbacher's Theorem: PGL(n,q) form a.. - Cameron (1997) (Correct)
....(or recognition) and the study of configurations or subsets. There is no sharp dividing line between the two, and many questions blend from one to the other. For further information on permutation groups, see Wielandt [35] or Cameron [6] for classical groups, Artin [1] or Dieudonn e [11], or Kleidman and Liebeck [20] for their maximal subgroups; and for the finite simple groups, Gorenstein [14] or the A TLAS [9] or Carter [8] for the Lie theoretic viewpoint. 2 Aschbacher s Theorem Since the Classification of Finite Simple Groups was announced in 1980 (see Gorenstein [14] ....
J. Dieudonn'e, La G'eometrie des Groupes Classiques, Springer, Berlin, 1963.
Packing Planes in Four Dimensions and Other Mysteries - Sloane (1998) (3 citations) (Correct)
.... E F 2 is given by B( g 1 ; g 2 ) Q( g 1 g 2 ) Q( g 1 ) Q( g 2 ) for g 1 ; g 2 2 E, and so B( X(a) Y (b) X(a 0 ) Y (b 0 ) a Delta b 0 a 0 Delta b : 11) Then ( E; Q) is an orthogonal vector space of type Omega (2i; 2) and maximal Witt index (cf. [16]) The Clifford group L that we need is the normalizer of E in O. This has order 2 i 2 i 2 (2 i Gamma 1) Pi i Gamma1 j=1 (4 j Gamma 1) cf. 9] Section 2) For i = 3 the order is 5160960: this is the group mentioned at the end of the last section. L is generated by E, all permutation ....
J. A. Dieudonn'e, La G'eom'etrie des Groupes Classiques, Springer-Verlag, Berlin, 1971.
A Geometric Definition Of Lie Derivative For Spinor.. - Fatibene, Ferraris.. (1995) (Correct)
....is due to E. Cartan in 1913 (cf. 4] in his researches on the linear representations of some simple Lie groups. A pretty nice and detailed algebraic theory was given later by C. Chevalley [5] and other papers on Clifford algebras and spinor groups were published, in particular by J. Dieudonn e [6], Atiyah, Bott, Shapiro [7] Milnor [8] Spinors on curved space time manifolds were introduced and used since 1928 by physicists. In a series of very important papers Yvette Kosmann [9,10,11,12] introduced the notion of Lie derivative for spinor fields on spin manifolds and the study of the ....
Dieudonn'e, J., (1963), La g'eometri'e des groupes classiques, deuxi`eme 'edition, Springer--Verlag, Berlin.
Automorphisms and quasi-conformal mappings of Heisenberg-type.. - Barbano (1998) (Correct)
....We denote this group by SU (2; H ) and observe that, since it contains the measure preserving maps of the kind OE h (X) h Delta x 1 ; x 2 Delta h Gamma1 ) h 2 GL(1; H ) it is non compact. A detailed discussion of these forms and their corresponding orthogonal groups can be found in ([5], chapter I) Finall we observe that the automorphisms acting non trivially on the center, contain a group isomorphic to the multiplicative group GL(1; H ) given by the maps M h (X) x 1 Delta h; h Gamma1 Delta x 2 ) h 2 GL(1; H ) Proposition 4.2. For i = 5; 6; 7 the groups Aut(N i ) 0 ....
Dieudonn'e, J., "La G'eom'etrie des Groupes Classiques, " Springer, New York, 1963.
Haar Measure on Linear Groups Over Local Skew Fields - Glöckner (1996) (Correct)
....on G 1 , then the image of 1 under is a Haar measure on G 2 . The conclusion of the corollary shows p 1 = p 2 . 3 An interesting special case is stated in Corollary 4.10. 3 For n1 ;n22 , this also follows from general investigations on the isomorphy problem of linear groups, cf. Dieudonn e [5], which show that the local fields K1 and K2 are algebraically isomorphic or antiisomorphic. This actually implies q1 =q2 in the commutative case, see Glockner [7] 174 Gl ockner Lemma 4.9. Let F be a commutative field, where charF 6= 2 , and n 2 N . Then Delta 2 : f diag(ff 1 ; ff n ....
Dieudonn'e, J. A., "La G'eom'etrie des Groupes Classiques," SpringerVerlag, Berlin etc., 1971.
Structure Of Hyperbolic Unitary Groups - I. Elementary Subgroups - Bak, Vavilov (2000) (Correct)
.... any form ideal (I; Gamma) the corresponding elementary subgroup EU(2n; I; Gamma) is normal in the hyperbolic unitary group U(2n; R; Moreover, EU(2n; I; Gamma) EU(2n; R; CU(2n; I; Gamma) where CU(2n; I; Gamma) is the full congruence subgroup of level (I; Gamma) 1 We refer to [Di], HO M] Md2] Md3] for a description of the earlier stages of development. For the linear groups the old era ended with [Ba1] BMS] Ba2] The thesis [B1] was not published and was not easily available, especially in Russia and China. This did a lot of harm. In fact, many works were ....
Dieudonn'e J., La g'eom'etrie des groupes classiques, 3rd ed, Springer, Berlin et al., 1971.
A Group-Theoretic Framework for the Construction.. - Calderbank.. (1997) (4 citations) (Correct)
.... 2 is given by B( g 1 ; g 2 ) Q( g 1 g 2 ) Q( g 1 ) Q( g 2 ) for g 1 ; g 2 2 E, and so B( X(a) Y (b) X(a 0 ) Y (b 0 ) a Delta b 0 a 0 Delta b : 5) Then ( E; Q) is an orthogonal vector space of type Omega (2i; 2) and maximal Witt index (cf. [12]) The normalizer of E in O is a certain Clifford group L, of order 2 i 2 i 2 (2 i Gamma 1) Pi i Gamma1 j=1 (4 j Gamma 1) cf. CCKS] Section 2) L is generated by E, all permutation matrices G(A; a) 2 O : e u e Au a , u 2 U , where A is an invertible i Theta i matrix over F 2 ....
J. A. Dieudonn'e, La G'eom'etrie des Groupes Classiques, Springer-Verlag, Berlin, 1971.
Reconstructing Simple Group Actions - Kantor, Penttila (Correct)
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J. Dieudonn'e, La g'eom'etrie des groupes classiques. Springer, Berlin-Gottingen -Heidelberg 1963.
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