Representations of Lie Groups and Lie Algebras

1985 ◽  
pp. 252-263
Author(s):  
Bartel Leenert van der Waerden
Keyword(s):  
Lie Groups ◽  
Lie Algebras ◽  
Representations Of Lie Groups

scholarly journals Extensions of Representations of Lie Groups and Lie Algebras, I

1957 ◽  
Vol 79 (4) ◽  
pp. 924 ◽  
Author(s):  
G. Hochschild ◽  
G. D. Mostow
Keyword(s):  
Lie Groups ◽  
Lie Algebras ◽  
Representations Of Lie Groups

Infinitely divisible projective representations of the Lie algebras

1972 ◽  
Vol 72 (3) ◽  
pp. 357-368 ◽  
Author(s):  
D. Mathon
Keyword(s):  
Lie Groups ◽  
Lie Algebras ◽  
Algebraic Method ◽  
Group Cohomology ◽  
Continuity Condition ◽  
Group Representations ◽  
Infinitely Divisible ◽  
Projective Representations ◽  
One To One ◽  
Representations Of Lie Groups

Infinitely divisible group representations were first defined by Streater(1) as an important concept closely related to continuous tensor product. Araki(2) analysed the factorizable representations of Lie groups and obtained a generalization of the Levy–Khinchine formula. A similar concept for Lie algebras was defined and studied by Streater in (3). Although the definition is not strictly an infinitesimal analogue of infinitely divisible representations of Lie groups, the results of (3) in the cohomological formulation are very similar to Araki's main theorem. Parthasarathy and Schmidt(4) generalized the concept of infinite divisibifity to the projective representations of locally compact groups and obtained a one-to-one correspondence between infinitely divisible projective representations and 1-co-cycles in the group cohomology with coefficients in a Hubert space. A similar generalization for Lie algebras is studied in the present paper. Infinitely divisible projective representations of Lie algebras are studied by a purely algebraic method, independently of (4) (since not all our projective representations are necessarily integrable). As expected, a one-to-one relation is obtained between the infinitely divisible projective representations and 1-co-cycles in the cohomology on the corresponding enveloping algebra with coefficients in a Hilbert space. The present problem is simpler than the group case since there is no continuity condition on the multiplier in a Lie algebra. A similar algebraic method was used in a discussion of infinitely divisible representations of canonical anticommutation relations (9).

Lie Groups, Lie Algebras, Cohomology and some Applications in Physics

1995 ◽  
Author(s):  
Josi A. de Azcárraga ◽  
Josi M. Izquierdo
Keyword(s):  
Lie Groups ◽  
Lie Algebras

scholarly journals Representations of complex semisimple Lie groups and Lie algebras

1966 ◽  
Vol 72 (3) ◽  
pp. 522-526 ◽  
Author(s):  
K. R. Parthasarathy ◽  
R. Ranga Rao ◽  
V. S. Varadarajan
Keyword(s):  
Lie Groups ◽  
Lie Algebras ◽  
Semisimple Lie Groups ◽  
Complex Semisimple
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