The Clifford algebra and the Spinor group of a Hilbert space

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1. W. Ambrose [1] Structure theorems for a special class of Banach algebras. Trans. AMS57 (1945) 364-386. Zbl0060.26906MR13235
2. M.F. Atiyah, R. Bott and A. Shapiro [2] Clifford modules. Topology vol. 3 suppl. 1 (1964) 3-38. Zbl0146.19001MR167985
3. M.F. Atiyah and I.M. Singer [3] Index of elliptic operators III. Ann. of Math.87 (1968) 546-604. Zbl0164.24301MR236952
4. R.J. Blattner [4] Automorphic group representations. Pacific J. Math.8 (1958) 665-677. Zbl0087.32001MR103421
5. N. Bourbaki [5] Algèbre, chapitre 9. Hermann1959. Zbl0102.25503
6. C. Chevalley [6] The algebraic theory of spinors. Columbia University Press, New York1954. Zbl0057.25901MR60497
7. Ja L. Dalec'kii [7] Infinite dimensional elliptic operators and parabolic equations connected with them. Russian Math. Surveys29 (1970) no 4, 1-53. Zbl0164.41304
8. J. Dieudonné [8] Eléments d'analyse, 2. Gauthiers-Villars1968. Zbl0189.05502
9. J. Dixmier [9] Les algèbres d'opérateurs dans l'espace hilbertien (algèbres de von Neumann), deuxième édition. Gauthier-Villars1969. Zbl0175.43801MR352996
10. S. Doplicher and R.T. Powers [10] On the simplicity of the even CAR algebra and free field models. Commun. Math. Phys.7 (1968) 77-79. Zbl0173.29804MR225543
11. A. Guichardet [11] Produits tensoriels infinis et représentations des relations d'anticommutation. Ann. Scient. Ec. Norm. Sup. (3) 83 (1966) 1-52. Zbl0154.38905MR205097
12. A. Haefliger [12] Sur l'extension du groupe structural d'un espace fibré. C. R. Acad. Sci. Paris243 (1956) 558-560. Zbl0070.40001MR84775
13. V.L. Hansen [13] Some theorems on direct limits of expanding sequences of manifolds. Math. Scand.29 (1971) 5-36. Zbl0229.58005MR319206
14. P. De La Harpe [14] Classical Banach-Lie algebras and Banach-Lie groups in Hilbert space. Springer Lecture Notes, 285 (1972). Zbl0256.22015MR476820
15. F. Hirzebruch [15] Topological methods in algebraic geometry. Third edition, Springer1966. Zbl0138.42001MR1335917
16. N. Jacobson [16] Lie algebras. Interscience1962. Zbl0121.27504MR143793
17. M. Karoubi [17] Algèbres de Clifford et K-théorie. Ann. Scient. Ec. Norm. Sup. (4) 1 (1968) 161-270. Zbl0194.24101MR238927
18. U. Koschorke [18] Infinite dimensional K-theory and characteristic classes of Fredholm bundle maps. Global Analysis, Berkeley, July 1968. Proc Sympos. Pure Math., XV (1970) 95-133. Zbl0207.53602MR279838
19. M. Lazard [19] Groupes différentiables. 'Neuvième leçon' of a course to be published in book-form. 
20. J. Milnor [20] Spin structures on manifolds. Enseignement Math. (2) 9 (1963) 198-203. Zbl0116.40403MR157388
21. R.S. Palais [21 ] Homotopy theory of infinite dimensional manifolds. Topology5 (1966) 1-16. Zbl0138.18302MR189028
22. C.R. Putnam and A. Wintner [22] The orthogonal group in Hilbert space. Amer. J. Math.74 (1952) 52-78 Zbl0049.35502MR45121
23. D. Shale and W.F. Stinespring [23] Spinor representations of infinite orthogonal groups. J. Math. Mech.14 (1965) 315-322. Zbl0132.36003MR173163
24. J. Slawny [24] Representations of canonical anticommutation relations and implementability of canonical transformations. Thesis, The Weizmann Institute of Science, Rehovot1969. Zbl0219.46047
25. J. Slawny [25] Same title. Commun. Math. Phys.22 (1971) 104-114. Zbl0219.46047
26. E. Størmer [26] The even CAR-algebra. Commun. Math. Phys.16 (1970) 136-137. Zbl0187.38503MR269232

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